diff --git a/src/librustc_data_structures/indexed_set.rs b/src/librustc_data_structures/indexed_set.rs
index d4da1bb3601df..65fdf10a86d13 100644
--- a/src/librustc_data_structures/indexed_set.rs
+++ b/src/librustc_data_structures/indexed_set.rs
@@ -19,6 +19,20 @@ use bitslice::{bitwise, Union, Subtract, Intersect};
 use indexed_vec::Idx;
 use rustc_serialize;
 
+/// This is implemented by all the index sets so that IdxSet::union() can be
+/// passed any type of index set.
+pub trait UnionIntoIdxSet<T: Idx> {
+    // Performs `other = other | self`.
+    fn union_into(&self, other: &mut IdxSet<T>) -> bool;
+}
+
+/// This is implemented by all the index sets so that IdxSet::subtract() can be
+/// passed any type of index set.
+pub trait SubtractFromIdxSet<T: Idx> {
+    // Performs `other = other - self`.
+    fn subtract_from(&self, other: &mut IdxSet<T>) -> bool;
+}
+
 /// Represents a set of some element type E, where each E is identified by some
 /// unique index type `T`.
 ///
@@ -164,48 +178,14 @@ impl<T: Idx> IdxSet<T> {
 
     /// Set `self = self | other` and return true if `self` changed
     /// (i.e., if new bits were added).
-    pub fn union(&mut self, other: &IdxSet<T>) -> bool {
-        bitwise(self.words_mut(), other.words(), &Union)
-    }
-
-    /// Like `union()`, but takes a `SparseIdxSet` argument.
-    fn union_sparse(&mut self, other: &SparseIdxSet<T>) -> bool {
-        let mut changed = false;
-        for elem in other.iter() {
-            changed |= self.add(&elem);
-        }
-        changed
-    }
-
-    /// Like `union()`, but takes a `HybridIdxSet` argument.
-    pub fn union_hybrid(&mut self, other: &HybridIdxSet<T>) -> bool {
-        match other {
-            HybridIdxSet::Sparse(sparse, _) => self.union_sparse(sparse),
-            HybridIdxSet::Dense(dense, _) => self.union(dense),
-        }
+    pub fn union(&mut self, other: &impl UnionIntoIdxSet<T>) -> bool {
+        other.union_into(self)
     }
 
     /// Set `self = self - other` and return true if `self` changed.
     /// (i.e., if any bits were removed).
-    pub fn subtract(&mut self, other: &IdxSet<T>) -> bool {
-        bitwise(self.words_mut(), other.words(), &Subtract)
-    }
-
-    /// Like `subtract()`, but takes a `SparseIdxSet` argument.
-    fn subtract_sparse(&mut self, other: &SparseIdxSet<T>) -> bool {
-        let mut changed = false;
-        for elem in other.iter() {
-            changed |= self.remove(&elem);
-        }
-        changed
-    }
-
-    /// Like `subtract()`, but takes a `HybridIdxSet` argument.
-    pub fn subtract_hybrid(&mut self, other: &HybridIdxSet<T>) -> bool {
-        match other {
-            HybridIdxSet::Sparse(sparse, _) => self.subtract_sparse(sparse),
-            HybridIdxSet::Dense(dense, _) => self.subtract(dense),
-        }
+    pub fn subtract(&mut self, other: &impl SubtractFromIdxSet<T>) -> bool {
+        other.subtract_from(self)
     }
 
     /// Set `self = self & other` and return true if `self` changed.
@@ -223,6 +203,18 @@ impl<T: Idx> IdxSet<T> {
     }
 }
 
+impl<T: Idx> UnionIntoIdxSet<T> for IdxSet<T> {
+    fn union_into(&self, other: &mut IdxSet<T>) -> bool {
+        bitwise(other.words_mut(), self.words(), &Union)
+    }
+}
+
+impl<T: Idx> SubtractFromIdxSet<T> for IdxSet<T> {
+    fn subtract_from(&self, other: &mut IdxSet<T>) -> bool {
+        bitwise(other.words_mut(), self.words(), &Subtract)
+    }
+}
+
 pub struct Iter<'a, T: Idx> {
     cur: Option<(Word, usize)>,
     iter: iter::Enumerate<slice::Iter<'a, Word>>,
@@ -308,6 +300,26 @@ impl<T: Idx> SparseIdxSet<T> {
     }
 }
 
+impl<T: Idx> UnionIntoIdxSet<T> for SparseIdxSet<T> {
+    fn union_into(&self, other: &mut IdxSet<T>) -> bool {
+        let mut changed = false;
+        for elem in self.iter() {
+            changed |= other.add(&elem);
+        }
+        changed
+    }
+}
+
+impl<T: Idx> SubtractFromIdxSet<T> for SparseIdxSet<T> {
+    fn subtract_from(&self, other: &mut IdxSet<T>) -> bool {
+        let mut changed = false;
+        for elem in self.iter() {
+            changed |= other.remove(&elem);
+        }
+        changed
+    }
+}
+
 pub struct SparseIter<'a, T: Idx> {
     iter: slice::Iter<'a, T>,
 }
@@ -411,6 +423,24 @@ impl<T: Idx> HybridIdxSet<T> {
     }
 }
 
+impl<T: Idx> UnionIntoIdxSet<T> for HybridIdxSet<T> {
+    fn union_into(&self, other: &mut IdxSet<T>) -> bool {
+        match self {
+            HybridIdxSet::Sparse(sparse, _) => sparse.union_into(other),
+            HybridIdxSet::Dense(dense, _) => dense.union_into(other),
+        }
+    }
+}
+
+impl<T: Idx> SubtractFromIdxSet<T> for HybridIdxSet<T> {
+    fn subtract_from(&self, other: &mut IdxSet<T>) -> bool {
+        match self {
+            HybridIdxSet::Sparse(sparse, _) => sparse.subtract_from(other),
+            HybridIdxSet::Dense(dense, _) => dense.subtract_from(other),
+        }
+    }
+}
+
 pub enum HybridIter<'a, T: Idx> {
     Sparse(SparseIter<'a, T>),
     Dense(Iter<'a, T>),
diff --git a/src/librustc_mir/dataflow/at_location.rs b/src/librustc_mir/dataflow/at_location.rs
index 0dfc5b5b4b7e0..1f7faa21a12c0 100644
--- a/src/librustc_mir/dataflow/at_location.rs
+++ b/src/librustc_mir/dataflow/at_location.rs
@@ -129,8 +129,8 @@ where
         F: FnOnce(Iter<BD::Idx>),
     {
         let mut curr_state = self.curr_state.clone();
-        curr_state.union_hybrid(&self.stmt_gen);
-        curr_state.subtract_hybrid(&self.stmt_kill);
+        curr_state.union(&self.stmt_gen);
+        curr_state.subtract(&self.stmt_kill);
         f(curr_state.iter());
     }
 }
@@ -193,8 +193,8 @@ impl<BD> FlowsAtLocation for FlowAtLocation<BD>
     }
 
     fn apply_local_effect(&mut self, _loc: Location) {
-        self.curr_state.union_hybrid(&self.stmt_gen);
-        self.curr_state.subtract_hybrid(&self.stmt_kill);
+        self.curr_state.union(&self.stmt_gen);
+        self.curr_state.subtract(&self.stmt_kill);
     }
 }
 
diff --git a/src/librustc_mir/dataflow/mod.rs b/src/librustc_mir/dataflow/mod.rs
index 598e827b2564e..48d349978686d 100644
--- a/src/librustc_mir/dataflow/mod.rs
+++ b/src/librustc_mir/dataflow/mod.rs
@@ -241,8 +241,8 @@ impl<'b, 'a: 'b, 'tcx: 'a, BD> PropagationContext<'b, 'a, 'tcx, BD> where BD: Bi
                 let sets = self.builder.flow_state.sets.for_block(bb.index());
                 debug_assert!(in_out.words().len() == sets.on_entry.words().len());
                 in_out.overwrite(sets.on_entry);
-                in_out.union_hybrid(sets.gen_set);
-                in_out.subtract_hybrid(sets.kill_set);
+                in_out.union(sets.gen_set);
+                in_out.subtract(sets.kill_set);
             }
             self.builder.propagate_bits_into_graph_successors_of(
                 in_out, (bb, bb_data), &mut dirty_queue);
@@ -534,8 +534,8 @@ impl<'a, E:Idx> BlockSets<'a, E> {
     }
 
     fn apply_local_effect(&mut self) {
-        self.on_entry.union_hybrid(&self.gen_set);
-        self.on_entry.subtract_hybrid(&self.kill_set);
+        self.on_entry.union(self.gen_set);
+        self.on_entry.subtract(self.kill_set);
     }
 }
 
diff --git a/src/librustc_mir/transform/rustc_peek.rs b/src/librustc_mir/transform/rustc_peek.rs
index 63675f056ab78..eda7de0fd79d4 100644
--- a/src/librustc_mir/transform/rustc_peek.rs
+++ b/src/librustc_mir/transform/rustc_peek.rs
@@ -209,8 +209,8 @@ fn each_block<'a, 'tcx, O>(tcx: TyCtxt<'a, 'tcx, 'tcx>,
             &mut sets, Location { block: bb, statement_index: j });
         results.0.operator.statement_effect(
             &mut sets, Location { block: bb, statement_index: j });
-        sets.on_entry.union_hybrid(sets.gen_set);
-        sets.on_entry.subtract_hybrid(sets.kill_set);
+        sets.on_entry.union(sets.gen_set);
+        sets.on_entry.subtract(sets.kill_set);
     }
 
     results.0.operator.before_terminator_effect(