diff --git a/src/par_iter/chain.rs b/src/par_iter/chain.rs
index 34b33778c..f7fd24f30 100644
--- a/src/par_iter/chain.rs
+++ b/src/par_iter/chain.rs
@@ -29,8 +29,8 @@ impl<A, B> ParallelIterator for ChainIter<A, B>
     fn drive_unindexed<C>(self, consumer: C) -> C::Result
         where C: UnindexedConsumer<Self::Item>
     {
-        let a = self.a.drive_unindexed(consumer.split_off());
-        let b = self.b.drive_unindexed(consumer.split_off());
+        let a = self.a.drive_unindexed(consumer.split_off_left());
+        let b = self.b.drive_unindexed(consumer.split_off_left());
         consumer.to_reducer().reduce(a, b)
     }
 
diff --git a/src/par_iter/collect/consumer.rs b/src/par_iter/collect/consumer.rs
index 37e21d0f0..aa1b84779 100644
--- a/src/par_iter/collect/consumer.rs
+++ b/src/par_iter/collect/consumer.rs
@@ -90,7 +90,7 @@ impl<'c, ITEM: Send + 'c> Folder<ITEM> for CollectFolder<'c, ITEM> {
 /// Pretend to be unindexed for `special_collect_into`,
 /// but we should never actually get used that way...
 impl<'c, ITEM: Send + 'c> UnindexedConsumer<ITEM> for CollectConsumer<'c, ITEM> {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         unreachable!("CollectConsumer must be indexed!")
     }
     fn to_reducer(&self) -> Self::Reducer {
diff --git a/src/par_iter/filter.rs b/src/par_iter/filter.rs
index cc5458a18..396337254 100644
--- a/src/par_iter/filter.rs
+++ b/src/par_iter/filter.rs
@@ -104,8 +104,8 @@ impl<'f, ITEM, C, FILTER_OP: 'f> UnindexedConsumer<ITEM> for FilterConsumer<'f,
     where C: UnindexedConsumer<ITEM>,
           FILTER_OP: Fn(&ITEM) -> bool + Sync
 {
-    fn split_off(&self) -> Self {
-        FilterConsumer::new(self.base.split_off(), &self.filter_op)
+    fn split_off_left(&self) -> Self {
+        FilterConsumer::new(self.base.split_off_left(), &self.filter_op)
     }
 
     fn to_reducer(&self) -> Self::Reducer {
diff --git a/src/par_iter/filter_map.rs b/src/par_iter/filter_map.rs
index be4dd8e2e..af9549b54 100644
--- a/src/par_iter/filter_map.rs
+++ b/src/par_iter/filter_map.rs
@@ -107,8 +107,8 @@ impl<'f, ITEM, MAPPED_ITEM, C, FILTER_OP> UnindexedConsumer<ITEM>
     where C: UnindexedConsumer<MAPPED_ITEM>,
           FILTER_OP: Fn(ITEM) -> Option<MAPPED_ITEM> + Sync + 'f
 {
-    fn split_off(&self) -> Self {
-        FilterMapConsumer::new(self.base.split_off(), &self.filter_op)
+    fn split_off_left(&self) -> Self {
+        FilterMapConsumer::new(self.base.split_off_left(), &self.filter_op)
     }
 
     fn to_reducer(&self) -> Self::Reducer {
diff --git a/src/par_iter/find.rs b/src/par_iter/find.rs
index c43180f6e..85c082aa0 100644
--- a/src/par_iter/find.rs
+++ b/src/par_iter/find.rs
@@ -40,7 +40,7 @@ impl<'f, ITEM, FIND_OP: 'f> Consumer<ITEM> for FindConsumer<'f, FIND_OP>
     }
 
     fn split_at(self, _index: usize) -> (Self, Self, Self::Reducer) {
-        (self.split_off(), self, FindReducer)
+        (self.split_off_left(), self, FindReducer)
     }
 
     fn into_folder(self) -> Self::Folder {
@@ -61,7 +61,7 @@ impl<'f, ITEM, FIND_OP: 'f> UnindexedConsumer<ITEM> for FindConsumer<'f, FIND_OP
     where ITEM: Send,
           FIND_OP: Fn(&ITEM) -> bool + Sync
 {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         FindConsumer::new(self.find_op, self.found)
     }
 
diff --git a/src/par_iter/find_first_last/mod.rs b/src/par_iter/find_first_last/mod.rs
index c2c721cb7..6e0cf902f 100644
--- a/src/par_iter/find_first_last/mod.rs
+++ b/src/par_iter/find_first_last/mod.rs
@@ -99,7 +99,7 @@ impl<'f, ITEM, FIND_OP> Consumer<ITEM> for FindConsumer<'f, FIND_OP>
 
     fn split_at(self, _index: usize) -> (Self, Self, Self::Reducer) {
         let dir = self.match_position;
-        (self.split_off(),
+        (self.split_off_left(),
          self,
          FindReducer { match_position: dir })
     }
@@ -127,7 +127,7 @@ impl<'f, ITEM, FIND_OP> UnindexedConsumer<ITEM> for FindConsumer<'f, FIND_OP>
     where ITEM: Send,
           FIND_OP: Fn(&ITEM) -> bool + Sync
 {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         // Upper bound for one consumer will be lower bound for the other. This
         // overlap is okay, because only one of the bounds will be used for
         // comparing against best_found; the other is kept only to be able to
@@ -139,10 +139,6 @@ impl<'f, ITEM, FIND_OP> UnindexedConsumer<ITEM> for FindConsumer<'f, FIND_OP>
         // consumer to stop working when the other finds a better match, but the
         // reducer ensures that the best answer is still returned (see the test
         // above).
-        //
-        // This code assumes that the caller of split_off will use the result as
-        // the *left* side of this iterator, and the remainder of self as the
-        // *right* side.
         let old_lower_bound = self.lower_bound.get();
         let median = old_lower_bound + ((self.upper_bound - old_lower_bound) / 2);
         self.lower_bound.set(median);
diff --git a/src/par_iter/find_first_last/test.rs b/src/par_iter/find_first_last/test.rs
index 08e3989ae..c284001c8 100644
--- a/src/par_iter/find_first_last/test.rs
+++ b/src/par_iter/find_first_last/test.rs
@@ -9,18 +9,19 @@ fn same_range_first_consumers_return_correct_answer() {
 
     // We save a consumer that will be far to the right of the main consumer (and therefore not
     // sharing an index range with that consumer) for fullness testing
-    let consumer = far_right_consumer.split_off();
+    let consumer = far_right_consumer.split_off_left();
 
     // split until we have an indivisible range
     let bits_in_usize = usize::min_value().count_zeros();
+
     for _ in 0..bits_in_usize {
-        consumer.split_off();
+        consumer.split_off_left();
     }
 
     let reducer = consumer.to_reducer();
     // the left and right folders should now have the same range, having
     // exhausted the resolution of usize
-    let left_folder = consumer.split_off().into_folder();
+    let left_folder = consumer.split_off_left().into_folder();
     let right_folder = consumer.into_folder();
 
     let left_folder = left_folder.consume(0).consume(1);
@@ -42,20 +43,20 @@ fn same_range_last_consumers_return_correct_answer() {
 
     // We save a consumer that will be far to the left of the main consumer (and therefore not
     // sharing an index range with that consumer) for fullness testing
-    let far_left_consumer = consumer.split_off();
+    let far_left_consumer = consumer.split_off_left();
 
     // split until we have an indivisible range
     let bits_in_usize = usize::min_value().count_zeros();
     for _ in 0..bits_in_usize {
-        consumer.split_off();
+        consumer.split_off_left();
     }
 
     let reducer = consumer.to_reducer();
-    // due to the exact calculation in split_off, the very last consumer has a
+    // due to the exact calculation in split_off_left, the very last consumer has a
     // range of width 2, so we use the second-to-last consumer instead to get
     // the same boundary on both folders
-    let consumer = consumer.split_off();
-    let left_folder = consumer.split_off().into_folder();
+    let consumer = consumer.split_off_left();
+    let left_folder = consumer.split_off_left().into_folder();
     let right_folder = consumer.into_folder();
     let right_folder = right_folder.consume(2).consume(3);
     assert_eq!(left_folder.boundary, right_folder.boundary);
diff --git a/src/par_iter/flat_map.rs b/src/par_iter/flat_map.rs
index e2b825108..cc7ca5eb7 100644
--- a/src/par_iter/flat_map.rs
+++ b/src/par_iter/flat_map.rs
@@ -73,8 +73,8 @@ impl<'m, ITEM, MAPPED_ITEM, C, MAP_OP> Consumer<ITEM> for FlatMapConsumer<'m, C,
     }
 
     fn split_at(self, _index: usize) -> (Self, Self, C::Reducer) {
-        (FlatMapConsumer::new(self.base.split_off(), self.map_op),
-         FlatMapConsumer::new(self.base.split_off(), self.map_op),
+        (FlatMapConsumer::new(self.base.split_off_left(), self.map_op),
+         FlatMapConsumer::new(self.base.split_off_left(), self.map_op),
          self.base.to_reducer())
     }
 
@@ -96,8 +96,8 @@ impl<'m, ITEM, MAPPED_ITEM, C, MAP_OP> UnindexedConsumer<ITEM> for FlatMapConsum
           MAP_OP: Fn(ITEM) -> MAPPED_ITEM + Sync,
           MAPPED_ITEM: IntoParallelIterator
 {
-    fn split_off(&self) -> Self {
-        FlatMapConsumer::new(self.base.split_off(), self.map_op)
+    fn split_off_left(&self) -> Self {
+        FlatMapConsumer::new(self.base.split_off_left(), self.map_op)
     }
 
     fn to_reducer(&self) -> Self::Reducer {
@@ -122,7 +122,7 @@ impl<'m, ITEM, MAPPED_ITEM, C, MAP_OP> Folder<ITEM> for FlatMapFolder<'m, C, MAP
     fn consume(self, item: ITEM) -> Self {
         let map_op = self.map_op;
         let par_iter = map_op(item).into_par_iter();
-        let result = par_iter.drive_unindexed(self.base.split_off());
+        let result = par_iter.drive_unindexed(self.base.split_off_left());
 
         // We expect that `previous` is `None`, because we drive
         // the cost up so high, but just in case.
diff --git a/src/par_iter/fold.rs b/src/par_iter/fold.rs
index ba9d3c9b0..a9bd472f3 100644
--- a/src/par_iter/fold.rs
+++ b/src/par_iter/fold.rs
@@ -106,8 +106,8 @@ impl<'r, U, ITEM, C, IDENTITY, FOLD_OP> UnindexedConsumer<ITEM>
           IDENTITY: Fn() -> U + Sync,
           U: Send
 {
-    fn split_off(&self) -> Self {
-        FoldConsumer { base: self.base.split_off(), ..*self }
+    fn split_off_left(&self) -> Self {
+        FoldConsumer { base: self.base.split_off_left(), ..*self }
     }
 
     fn to_reducer(&self) -> Self::Reducer {
diff --git a/src/par_iter/for_each.rs b/src/par_iter/for_each.rs
index 00321ce66..0eba94f80 100644
--- a/src/par_iter/for_each.rs
+++ b/src/par_iter/for_each.rs
@@ -29,7 +29,7 @@ impl<'f, OP, ITEM> Consumer<ITEM> for ForEachConsumer<'f, OP>
     }
 
     fn split_at(self, _index: usize) -> (Self, Self, NoopReducer) {
-        (self.split_off(), self.split_off(), NoopReducer)
+        (self.split_off_left(), self.split_off_left(), NoopReducer)
     }
 
     fn into_folder(self) -> Self {
@@ -53,7 +53,7 @@ impl<'f, OP, ITEM> Folder<ITEM> for ForEachConsumer<'f, OP>
 impl<'f, OP, ITEM> UnindexedConsumer<ITEM> for ForEachConsumer<'f, OP>
     where OP: Fn(ITEM) + Sync
 {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         ForEachConsumer { op: self.op }
     }
 
diff --git a/src/par_iter/internal.rs b/src/par_iter/internal.rs
index 60391f8c2..5500efab6 100644
--- a/src/par_iter/internal.rs
+++ b/src/par_iter/internal.rs
@@ -102,7 +102,10 @@ pub trait Reducer<Result> {
 
 /// A stateless consumer can be freely copied.
 pub trait UnindexedConsumer<ITEM>: Consumer<ITEM> {
-    fn split_off(&self) -> Self;
+    // The result of split_off_left should be used for the left side of the
+    // data it consumes, and the remaining consumer for the right side
+    // (this matters for methods like find_first).
+    fn split_off_left(&self) -> Self;
     fn to_reducer(&self) -> Self::Reducer;
 }
 
@@ -270,7 +273,7 @@ fn bridge_unindexed_producer_consumer<P, C>(mut splitter: Splitter,
         consumer.into_folder().complete()
     } else if let Some(right_producer) = splitter.try_unindexed(&mut producer) {
         let (reducer, left_consumer, right_consumer) =
-            (consumer.to_reducer(), consumer.split_off(), consumer);
+            (consumer.to_reducer(), consumer.split_off_left(), consumer);
         let (left_result, right_result) =
             join(|| bridge_unindexed_producer_consumer(splitter, producer, left_consumer),
                  || bridge_unindexed_producer_consumer(splitter, right_producer, right_consumer));
diff --git a/src/par_iter/map.rs b/src/par_iter/map.rs
index 19cbf8a25..19111c1ec 100644
--- a/src/par_iter/map.rs
+++ b/src/par_iter/map.rs
@@ -256,8 +256,8 @@ impl<'m, ITEM, C, MAP_OP> UnindexedConsumer<ITEM> for MapConsumer<'m, C, MAP_OP>
     where C: UnindexedConsumer<MAP_OP::Output>,
           MAP_OP: MapOp<ITEM>
 {
-    fn split_off(&self) -> Self {
-        MapConsumer::new(self.base.split_off(), &self.map_op)
+    fn split_off_left(&self) -> Self {
+        MapConsumer::new(self.base.split_off_left(), &self.map_op)
     }
 
     fn to_reducer(&self) -> Self::Reducer {
diff --git a/src/par_iter/mod.rs b/src/par_iter/mod.rs
index 135573f81..6189d5d17 100644
--- a/src/par_iter/mod.rs
+++ b/src/par_iter/mod.rs
@@ -629,9 +629,9 @@ pub trait ParallelIterator: Sized {
     /// statically. This can be used by consumers to trigger special fast
     /// paths. Therefore, if `Some(_)` is returned, this iterator must only
     /// use the (indexed) `Consumer` methods when driving a consumer, such
-    /// as `split_at()`. Calling `UnindexedConsumer::split_off()` or other
-    /// `UnindexedConsumer` methods -- or returning an inaccurate value --
-    /// may result in panics.
+    /// as `split_at()`. Calling `UnindexedConsumer::split_off_left()` or
+    /// other `UnindexedConsumer` methods -- or returning an inaccurate
+    /// value -- may result in panics.
     ///
     /// This is hidden & considered internal for now, until we decide
     /// whether it makes sense for a public API.  Right now it is only used
diff --git a/src/par_iter/noop.rs b/src/par_iter/noop.rs
index e4a12b018..6683ce903 100644
--- a/src/par_iter/noop.rs
+++ b/src/par_iter/noop.rs
@@ -37,7 +37,7 @@ impl<ITEM> Folder<ITEM> for NoopConsumer {
 }
 
 impl<ITEM> UnindexedConsumer<ITEM> for NoopConsumer {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         NoopConsumer
     }
 
diff --git a/src/par_iter/reduce.rs b/src/par_iter/reduce.rs
index 567cbb877..3f59a3791 100644
--- a/src/par_iter/reduce.rs
+++ b/src/par_iter/reduce.rs
@@ -81,7 +81,7 @@ impl<'r, REDUCE_OP, ITEM> UnindexedConsumer<ITEM> for ReduceConsumer<'r, REDUCE_
     where REDUCE_OP: ReduceOp<ITEM>,
           ITEM: Send
 {
-    fn split_off(&self) -> Self {
+    fn split_off_left(&self) -> Self {
         ReduceConsumer { reduce_op: self.reduce_op }
     }
 
diff --git a/src/par_iter/weight.rs b/src/par_iter/weight.rs
index 3751d19af..053d9f274 100644
--- a/src/par_iter/weight.rs
+++ b/src/par_iter/weight.rs
@@ -169,8 +169,8 @@ impl<C, ITEM> Consumer<ITEM> for WeightConsumer<C>
 impl<C, ITEM> UnindexedConsumer<ITEM> for WeightConsumer<C>
     where C: UnindexedConsumer<ITEM>
 {
-    fn split_off(&self) -> Self {
-        WeightConsumer::new(self.base.split_off(), self.weight)
+    fn split_off_left(&self) -> Self {
+        WeightConsumer::new(self.base.split_off_left(), self.weight)
     }
 
     fn to_reducer(&self) -> Self::Reducer {