diff --git a/core/Cargo.toml b/core/Cargo.toml
index a4f93198..64424b03 100644
--- a/core/Cargo.toml
+++ b/core/Cargo.toml
@@ -4,9 +4,10 @@ version = "0.0.1"
 workspace = ".."
 
 [dependencies]
+enum-set = { git = "https://github.com/rnewman/enum-set" }
+lazy_static = "0.2.2"
 num = "0.1.35"
 ordered-float = "0.4.0"
-lazy_static = "0.2.2"
 
 [dependencies.edn]
 path = "../edn"
diff --git a/core/src/lib.rs b/core/src/lib.rs
index 943a30d2..67b4d183 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -8,6 +8,8 @@
 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
 // specific language governing permissions and limitations under the License.
 
+extern crate enum_set;
+
 #[macro_use]
 extern crate lazy_static;
 extern crate ordered_float;
@@ -19,6 +21,9 @@ pub mod values;
 use std::collections::BTreeMap;
 use std::fmt;
 use std::rc::Rc;
+
+use enum_set::EnumSet;
+
 use self::ordered_float::OrderedFloat;
 use self::edn::NamespacedKeyword;
 
@@ -33,7 +38,8 @@ pub type Entid = i64;
 
 /// The attribute of each Mentat assertion has a :db/valueType constraining the value to a
 /// particular set.  Mentat recognizes the following :db/valueType values.
-#[derive(Clone,Copy,Debug,Eq,Hash,Ord,PartialOrd,PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, Hash, Ord, PartialOrd, PartialEq)]
+#[repr(u32)]
 pub enum ValueType {
     Ref,
     Boolean,
@@ -44,6 +50,32 @@ pub enum ValueType {
     Keyword,
 }
 
+impl ValueType {
+    pub fn all_enums() -> EnumSet<ValueType> {
+        // TODO: lazy_static.
+        let mut s = EnumSet::new();
+        s.insert(ValueType::Ref);
+        s.insert(ValueType::Boolean);
+        s.insert(ValueType::Instant);
+        s.insert(ValueType::Long);
+        s.insert(ValueType::Double);
+        s.insert(ValueType::String);
+        s.insert(ValueType::Keyword);
+        s
+    }
+}
+
+
+impl enum_set::CLike for ValueType {
+    fn to_u32(&self) -> u32 {
+        *self as u32
+    }
+
+    unsafe fn from_u32(v: u32) -> ValueType {
+        std::mem::transmute(v)
+    }
+}
+
 impl ValueType {
     pub fn to_edn_value(self) -> edn::Value {
         match self {
diff --git a/query-algebrizer/Cargo.toml b/query-algebrizer/Cargo.toml
index c21bc49b..bfa9ed84 100644
--- a/query-algebrizer/Cargo.toml
+++ b/query-algebrizer/Cargo.toml
@@ -4,6 +4,7 @@ version = "0.0.1"
 workspace = ".."
 
 [dependencies]
+enum-set = { git = "https://github.com/rnewman/enum-set" }
 error-chain = "0.8.1"
 
 [dependencies.mentat_core]
diff --git a/query-algebrizer/src/clauses/mod.rs b/query-algebrizer/src/clauses/mod.rs
index ca054d89..c980fd97 100644
--- a/query-algebrizer/src/clauses/mod.rs
+++ b/query-algebrizer/src/clauses/mod.rs
@@ -13,7 +13,6 @@ use std::cmp;
 use std::collections::{
     BTreeMap,
     BTreeSet,
-    HashSet,
 };
 
 use std::collections::btree_map::Entry;
@@ -59,6 +58,7 @@ use types::{
     QueryValue,
     SourceAlias,
     TableAlias,
+    ValueTypeSet,
 };
 
 mod inputs;
@@ -82,12 +82,6 @@ impl<T: Clone> RcCloned<T> for ::std::rc::Rc<T> {
     }
 }
 
-fn unit_type_set(t: ValueType) -> HashSet<ValueType> {
-    let mut s = HashSet::with_capacity(1);
-    s.insert(t);
-    s
-}
-
 trait Contains<K, T> {
     fn when_contains<F: FnOnce() -> T>(&self, k: &K, f: F) -> Option<T>;
 }
@@ -201,10 +195,11 @@ pub struct ConjoiningClauses {
     /// A map from var to type. Whenever a var maps unambiguously to two different types, it cannot
     /// yield results, so we don't represent that case here. If a var isn't present in the map, it
     /// means that its type is not known in advance.
-    pub known_types: BTreeMap<Variable, HashSet<ValueType>>,
+    /// Usually that state should be represented by `ValueTypeSet::Any`.
+    pub known_types: BTreeMap<Variable, ValueTypeSet>,
 
     /// A mapping, similar to `column_bindings`, but used to pull type tags out of the store at runtime.
-    /// If a var isn't present in `known_types`, it should be present here.
+    /// If a var isn't unit in `known_types`, it should be present here.
     pub extracted_types: BTreeMap<Variable, QualifiedAlias>,
 }
 
@@ -278,7 +273,7 @@ impl ConjoiningClauses {
                 // Pre-fill our type mappings with the types of the input bindings.
                 cc.known_types
                   .extend(types.iter()
-                               .map(|(k, v)| (k.clone(), unit_type_set(*v))));
+                               .map(|(k, v)| (k.clone(), ValueTypeSet::of_one(*v))));
                 cc
             },
         }
@@ -330,7 +325,7 @@ impl ConjoiningClauses {
     /// or integer" isn't good enough.
     pub fn known_type(&self, var: &Variable) -> Option<ValueType> {
         match self.known_types.get(var) {
-            Some(types) if types.len() == 1 => types.iter().next().cloned(),
+            Some(set) if set.is_unit() => set.exemplar(),
             _ => None,
         }
     }
@@ -443,16 +438,12 @@ impl ConjoiningClauses {
 
     /// Mark the given value as a long.
     pub fn constrain_var_to_long(&mut self, variable: Variable) {
-        self.narrow_types_for_var(variable, unit_type_set(ValueType::Long));
+        self.narrow_types_for_var(variable, ValueTypeSet::of_one(ValueType::Long));
     }
 
     /// Mark the given value as one of the set of numeric types.
     fn constrain_var_to_numeric(&mut self, variable: Variable) {
-        let mut numeric_types = HashSet::with_capacity(2);
-        numeric_types.insert(ValueType::Double);
-        numeric_types.insert(ValueType::Long);
-
-        self.narrow_types_for_var(variable, numeric_types);
+        self.narrow_types_for_var(variable, ValueTypeSet::of_numeric_types());
     }
 
     /// Constrains the var if there's no existing type.
@@ -462,9 +453,9 @@ impl ConjoiningClauses {
         // Is there an existing mapping for this variable?
         // Any known inputs have already been added to known_types, and so if they conflict we'll
         // spot it here.
-        if let Some(existing) = self.known_types.insert(variable.clone(), unit_type_set(this_type)) {
+        if let Some(existing) = self.known_types.insert(variable.clone(), ValueTypeSet::of_one(this_type)) {
             // There was an existing mapping. Does this type match?
-            if !existing.contains(&this_type) {
+            if !existing.contains(this_type) {
                 self.mark_known_empty(EmptyBecause::TypeMismatch(variable, existing, this_type));
             }
         }
@@ -477,21 +468,28 @@ impl ConjoiningClauses {
     /// actually move from a state in which a variable can have no type to one that can
     /// yield results! We never do so at present -- we carefully set-union types before we
     /// set-intersect them -- but this is worth bearing in mind.
-    pub fn broaden_types(&mut self, additional_types: BTreeMap<Variable, HashSet<ValueType>>) {
+    pub fn broaden_types(&mut self, additional_types: BTreeMap<Variable, ValueTypeSet>) {
         for (var, new_types) in additional_types {
             match self.known_types.entry(var) {
                 Entry::Vacant(e) => {
-                    if new_types.len() == 1 {
+                    if new_types.is_unit() {
                         self.extracted_types.remove(e.key());
                     }
                     e.insert(new_types);
                 },
                 Entry::Occupied(mut e) => {
-                    if e.get().is_empty() && self.empty_because.is_some() {
-                        panic!("Uh oh: we failed this pattern, probably because {:?} couldn't match, but now we're broadening its type.",
-                               e.get());
+                    let new;
+                    // Scoped borrow of `e`.
+                    {
+                        let existing_types = e.get();
+                        if existing_types.is_empty() &&  // The set is empty: no types are possible.
+                           self.empty_because.is_some() {
+                            panic!("Uh oh: we failed this pattern, probably because {:?} couldn't match, but now we're broadening its type.",
+                                   e.key());
+                        }
+                        new = existing_types.union(&new_types);
                     }
-                    e.get_mut().extend(new_types.into_iter());
+                    e.insert(new);
                 },
             }
         }
@@ -501,7 +499,7 @@ impl ConjoiningClauses {
     /// If no types are already known -- `var` could have any type -- then this is equivalent to
     /// simply setting the known types to `types`.
     /// If the known types don't intersect with `types`, mark the pattern as known-empty.
-    fn narrow_types_for_var(&mut self, var: Variable, types: HashSet<ValueType>) {
+    fn narrow_types_for_var(&mut self, var: Variable, types: ValueTypeSet) {
         if types.is_empty() {
             // We hope this never occurs; we should catch this case earlier.
             self.mark_known_empty(EmptyBecause::NoValidTypes(var));
@@ -515,10 +513,9 @@ impl ConjoiningClauses {
                 e.insert(types);
             },
             Entry::Occupied(mut e) => {
-                // TODO: we shouldn't need to clone here.
-                let intersected: HashSet<_> = types.intersection(e.get()).cloned().collect();
+                let intersected: ValueTypeSet = types.intersection(e.get());
                 if intersected.is_empty() {
-                    let mismatching_type = types.iter().next().unwrap().clone();
+                    let mismatching_type = types.exemplar().expect("types isn't none");
                     let reason = EmptyBecause::TypeMismatch(e.key().clone(),
                                                             e.get().clone(),
                                                             mismatching_type);
@@ -536,7 +533,7 @@ impl ConjoiningClauses {
 
     /// Restrict the sets of types for the provided vars to the provided types.
     /// See `narrow_types_for_var`.
-    pub fn narrow_types(&mut self, additional_types: BTreeMap<Variable, HashSet<ValueType>>) {
+    pub fn narrow_types(&mut self, additional_types: BTreeMap<Variable, ValueTypeSet>) {
         if additional_types.is_empty() {
             return;
         }
@@ -623,7 +620,7 @@ impl ConjoiningClauses {
                 &PatternValuePlace::Variable(ref v) => {
                     // Do we know that this variable can't be a string? If so, we don't need
                     // AllDatoms. None or String means it could be or definitely is.
-                    match self.known_types.get(v).map(|types| types.contains(&ValueType::String)) {
+                    match self.known_types.get(v).map(|types| types.contains(ValueType::String)) {
                         Some(false) => DatomsTable::Datoms,
                         _           => DatomsTable::AllDatoms,
                     }
@@ -769,7 +766,7 @@ impl ConjoiningClauses {
             return;
         }
         for (var, types) in self.known_types.iter() {
-            if types.len() == 1 {
+            if types.is_unit() {
                 self.extracted_types.remove(var);
             }
         }
diff --git a/query-algebrizer/src/clauses/or.rs b/query-algebrizer/src/clauses/or.rs
index d14dd9e1..971ff010 100644
--- a/query-algebrizer/src/clauses/or.rs
+++ b/query-algebrizer/src/clauses/or.rs
@@ -9,7 +9,10 @@
 // specific language governing permissions and limitations under the License.
 
 use std::collections::btree_map::Entry;
-use std::collections::BTreeSet;
+use std::collections::{
+    BTreeMap,
+    BTreeSet,
+};
 
 use mentat_core::{
     Schema,
@@ -41,6 +44,7 @@ use types::{
     EmptyBecause,
     QualifiedAlias,
     SourceAlias,
+    ValueTypeSet,
     VariableColumn,
 };
 
@@ -654,6 +658,21 @@ impl ConjoiningClauses {
             type_associations = type_needed.iter().cloned().collect();
         }
 
+        // Collect the new type information from the arms. There's some redundant work here --
+        // they already have all of the information from the parent.
+        // Note that we start with the first clause's type information.
+        {
+            let mut clauses = acc.iter();
+            let mut additional_types = clauses.next()
+                                              .expect("there to be at least one clause")
+                                              .known_types
+                                              .clone();
+            for cc in clauses {
+                union_types(&mut additional_types, &cc.known_types);
+            }
+            self.broaden_types(additional_types);
+        }
+
         let union = ComputedTable::Union {
             projection: projection,
             type_extraction: type_needed,
@@ -674,6 +693,43 @@ impl ConjoiningClauses {
     }
 }
 
+/// Helper to fold together a set of type maps.
+fn union_types(into: &mut BTreeMap<Variable, ValueTypeSet>,
+               additional_types: &BTreeMap<Variable, ValueTypeSet>) {
+    // We want the exclusive disjunction -- any variable not mentioned in both sets -- to default
+    // to ValueTypeSet::Any.
+    // This is necessary because we lazily populate known_types, so sometimes the type set will
+    // be missing a `ValueTypeSet::Any` for a variable, and we want to broaden rather than
+    // accidentally taking the other side's word for it!
+    // The alternative would be to exhaustively pre-fill `known_types` with all mentioned variables
+    // in the whole query, which is daunting.
+    let mut any: BTreeMap<Variable, ValueTypeSet>;
+    // Scoped borrow of `into`.
+    {
+        let i: BTreeSet<&Variable> = into.keys().collect();
+        let a: BTreeSet<&Variable> = additional_types.keys().collect();
+        any = i.symmetric_difference(&a)
+               .map(|v| ((*v).clone(), ValueTypeSet::any()))
+               .collect();
+    }
+
+    // Collect the additional types.
+    for (var, new_types) in additional_types {
+        match into.entry(var.clone()) {
+            Entry::Vacant(e) => {
+                e.insert(new_types.clone());
+            },
+            Entry::Occupied(mut e) => {
+                let new = e.get().union(&new_types);
+                e.insert(new);
+            },
+        }
+    }
+
+    // Blat in those that are disjoint.
+    into.append(&mut any);
+}
+
 #[cfg(test)]
 mod testing {
     extern crate mentat_query_parser;
diff --git a/query-algebrizer/src/clauses/pattern.rs b/query-algebrizer/src/clauses/pattern.rs
index 21e98138..65bcfd01 100644
--- a/query-algebrizer/src/clauses/pattern.rs
+++ b/query-algebrizer/src/clauses/pattern.rs
@@ -293,7 +293,6 @@ mod testing {
         add_attribute,
         associate_ident,
         ident,
-        unit_type_set,
     };
 
     use types::{
@@ -303,6 +302,7 @@ mod testing {
         QualifiedAlias,
         QueryValue,
         SourceAlias,
+        ValueTypeSet,
     };
 
     use algebrize;
@@ -801,7 +801,7 @@ mod testing {
 
         assert!(cc.is_known_empty());
         assert_eq!(cc.empty_because.unwrap(),
-                   EmptyBecause::TypeMismatch(y.clone(), unit_type_set(ValueType::String), ValueType::Boolean));
+                   EmptyBecause::TypeMismatch(y.clone(), ValueTypeSet::of_one(ValueType::String), ValueType::Boolean));
     }
 
     #[test]
@@ -839,7 +839,7 @@ mod testing {
 
         assert!(cc.is_known_empty());
         assert_eq!(cc.empty_because.unwrap(),
-                   EmptyBecause::TypeMismatch(x.clone(), unit_type_set(ValueType::Ref), ValueType::Boolean));
+                   EmptyBecause::TypeMismatch(x.clone(), ValueTypeSet::of_one(ValueType::Ref), ValueType::Boolean));
     }
 
     #[test]
@@ -854,8 +854,8 @@ mod testing {
         let e = Variable::from_valid_name("?e");
         let v = Variable::from_valid_name("?v");
         let cc = alg(&schema, query);
-        assert_eq!(cc.known_types.get(&e), Some(&unit_type_set(ValueType::Ref)));
-        assert_eq!(cc.known_types.get(&v), Some(&unit_type_set(ValueType::Boolean)));
+        assert_eq!(cc.known_types.get(&e), Some(&ValueTypeSet::of_one(ValueType::Ref)));
+        assert_eq!(cc.known_types.get(&v), Some(&ValueTypeSet::of_one(ValueType::Boolean)));
         assert!(!cc.extracted_types.contains_key(&e));
         assert!(!cc.extracted_types.contains_key(&v));
     }
diff --git a/query-algebrizer/src/clauses/predicate.rs b/query-algebrizer/src/clauses/predicate.rs
index 031d20be..fca10e9a 100644
--- a/query-algebrizer/src/clauses/predicate.rs
+++ b/query-algebrizer/src/clauses/predicate.rs
@@ -87,7 +87,6 @@ impl ConjoiningClauses {
 mod testing {
     use super::*;
 
-    use std::collections::HashSet;
     use mentat_core::attribute::Unique;
     use mentat_core::{
         Attribute,
@@ -115,6 +114,7 @@ mod testing {
         ColumnConstraint,
         EmptyBecause,
         QueryValue,
+        ValueTypeSet,
     };
 
     #[test]
@@ -159,7 +159,7 @@ mod testing {
         // After processing those two clauses, we know that ?y must be numeric, but not exactly
         // which type it must be.
         assert_eq!(None, cc.known_type(&y));      // Not just one.
-        let expected: HashSet<ValueType> = vec![ValueType::Double, ValueType::Long].into_iter().collect();
+        let expected = ValueTypeSet::of_numeric_types();
         assert_eq!(Some(&expected), cc.known_types.get(&y));
 
         let clauses = cc.wheres;
@@ -225,8 +225,7 @@ mod testing {
         assert!(cc.is_known_empty());
         assert_eq!(cc.empty_because.unwrap(),
                    EmptyBecause::TypeMismatch(y.clone(),
-                                              vec![ValueType::Double, ValueType::Long].into_iter()
-                                                                                      .collect(),
+                                              ValueTypeSet::of_numeric_types(),
                                               ValueType::String));
     }
 }
\ No newline at end of file
diff --git a/query-algebrizer/src/lib.rs b/query-algebrizer/src/lib.rs
index 4315a6dc..a890d065 100644
--- a/query-algebrizer/src/lib.rs
+++ b/query-algebrizer/src/lib.rs
@@ -8,6 +8,8 @@
 // CONDITIONS OF ANY KIND, either express or implied. See the License for the
 // specific language governing permissions and limitations under the License.
 
+extern crate enum_set;
+
 #[macro_use]
 extern crate error_chain;
 
diff --git a/query-algebrizer/src/types.rs b/query-algebrizer/src/types.rs
index 8652d793..a9988a67 100644
--- a/query-algebrizer/src/types.rs
+++ b/query-algebrizer/src/types.rs
@@ -9,14 +9,17 @@
 // specific language governing permissions and limitations under the License.
 
 use std::collections::BTreeSet;
-use std::collections::HashSet;
-
 use std::fmt::{
     Debug,
     Formatter,
     Result,
 };
 
+use enum_set::{
+    CLike,
+    EnumSet,
+};
+
 use mentat_core::{
     Entid,
     TypedValue,
@@ -411,7 +414,7 @@ impl Debug for ColumnConstraint {
 #[derive(PartialEq, Clone)]
 pub enum EmptyBecause {
     // Var, existing, desired.
-    TypeMismatch(Variable, HashSet<ValueType>, ValueType),
+    TypeMismatch(Variable, ValueTypeSet, ValueType),
     NoValidTypes(Variable),
     NonNumericArgument,
     NonStringFulltextValue,
@@ -461,4 +464,89 @@ impl Debug for EmptyBecause {
             },
         }
     }
+}
+
+trait EnumSetExtensions<T: CLike + Clone> {
+    /// Return a set containing both `x` and `y`.
+    fn of_both(x: T, y: T) -> EnumSet<T>;
+
+    /// Return a clone of `self` with `y` added.
+    fn with(&self, y: T) -> EnumSet<T>;
+}
+
+impl<T: CLike + Clone> EnumSetExtensions<T> for EnumSet<T> {
+    /// Return a set containing both `x` and `y`.
+    fn of_both(x: T, y: T) -> Self {
+        let mut o = EnumSet::new();
+        o.insert(x);
+        o.insert(y);
+        o
+    }
+
+    /// Return a clone of `self` with `y` added.
+    fn with(&self, y: T) -> EnumSet<T> {
+        let mut o = self.clone();
+        o.insert(y);
+        o
+    }
+}
+
+#[derive(Clone, Debug, Eq, PartialEq)]
+pub struct ValueTypeSet(pub EnumSet<ValueType>);
+
+impl Default for ValueTypeSet {
+    fn default() -> ValueTypeSet {
+        ValueTypeSet::any()
+    }
+}
+
+impl ValueTypeSet {
+    pub fn any() -> ValueTypeSet {
+        ValueTypeSet(ValueType::all_enums())
+    }
+
+    pub fn none() -> ValueTypeSet {
+        ValueTypeSet(EnumSet::new())
+    }
+
+    /// Return a set containing only `t`.
+    pub fn of_one(t: ValueType) -> ValueTypeSet {
+        let mut s = EnumSet::new();
+        s.insert(t);
+        ValueTypeSet(s)
+    }
+
+    /// Return a set containing `Double` and `Long`.
+    pub fn of_numeric_types() -> ValueTypeSet {
+        ValueTypeSet(EnumSet::of_both(ValueType::Double, ValueType::Long))
+    }
+}
+
+impl ValueTypeSet {
+    /// Returns a set containing all the types in this set and `other`.
+    pub fn union(&self, other: &ValueTypeSet) -> ValueTypeSet {
+        ValueTypeSet(self.0.union(other.0))
+    }
+
+    pub fn intersection(&self, other: &ValueTypeSet) -> ValueTypeSet {
+        ValueTypeSet(self.0.intersection(other.0))
+    }
+
+    /// Return an arbitrary type that's part of this set.
+    /// For a set containing a single type, this will be that type.
+    pub fn exemplar(&self) -> Option<ValueType> {
+        self.0.iter().next()
+    }
+
+    pub fn contains(&self, vt: ValueType) -> bool {
+        self.0.contains(&vt)
+    }
+
+    pub fn is_empty(&self) -> bool {
+        self.0.is_empty()
+    }
+
+    pub fn is_unit(&self) -> bool {
+        self.0.len() == 1
+    }
 }
\ No newline at end of file
diff --git a/query-translator/tests/translate.rs b/query-translator/tests/translate.rs
index 9d533b69..fef09d2a 100644
--- a/query-translator/tests/translate.rs
+++ b/query-translator/tests/translate.rs
@@ -466,3 +466,34 @@ fn test_order_by() {
                      ORDER BY `?y_value_type_tag` ASC, `?y` ASC, `?x` ASC");
     assert_eq!(args, vec![]);
 }
+
+#[test]
+fn test_complex_nested_or_join_type_projection() {
+    let mut schema = Schema::default();
+    associate_ident(&mut schema, NamespacedKeyword::new("page", "title"), 98);
+    add_attribute(&mut schema, 98, Attribute {
+        value_type: ValueType::String,
+        ..Default::default()
+    });
+
+    let input = r#"[:find [?y]
+                    :where
+                    (or
+                      (or
+                        [_ :page/title ?y])
+                      (or
+                        [_ :page/title ?y]))]"#;
+
+    let SQLQuery { sql, args } = translate(&schema, input);
+    assert_eq!(sql, "SELECT `c00`.`?y` AS `?y` \
+                     FROM (SELECT `datoms00`.v AS `?y` \
+                           FROM `datoms` AS `datoms00` \
+                           WHERE `datoms00`.a = 98 \
+                           UNION \
+                           SELECT `datoms01`.v AS `?y` \
+                           FROM `datoms` AS `datoms01` \
+                           WHERE `datoms01`.a = 98) \
+                           AS `c00` \
+                     LIMIT 1");
+    assert_eq!(args, vec![]);
+}
\ No newline at end of file