diff --git a/src/lib.rs b/src/lib.rs
index 7dc40370b..ec1bbca2a 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1075,7 +1075,6 @@ pub trait Itertools: Iterator {
     where
         J: IntoIterator,
         F: FnMut(&Self::Item, &J::Item) -> T,
-        T: merge_join::OrderingOrBool<Self::Item, J::Item>,
         Self: Sized,
     {
         merge_join_by(self, other, cmp_fn)
diff --git a/src/merge_join.rs b/src/merge_join.rs
index 1769aaf3a..c83159186 100644
--- a/src/merge_join.rs
+++ b/src/merge_join.rs
@@ -1,7 +1,7 @@
 use std::cmp::Ordering;
 use std::fmt;
-use std::iter::Fuse;
-use std::iter::{FusedIterator, Peekable};
+use std::iter::{Fuse, FusedIterator};
+use std::marker::PhantomData;
 
 use either::Either;
 
@@ -11,19 +11,9 @@ use crate::size_hint::{self, SizeHint};
 #[cfg(doc)]
 use crate::Itertools;
 
-pub trait MergePredicate<T> {
-    fn merge_pred(&mut self, a: &T, b: &T) -> bool;
-}
-
 #[derive(Clone, Debug)]
 pub struct MergeLte;
 
-impl<T: PartialOrd> MergePredicate<T> for MergeLte {
-    fn merge_pred(&mut self, a: &T, b: &T) -> bool {
-        a <= b
-    }
-}
-
 /// An iterator adaptor that merges the two base iterators in ascending order.
 /// If both base iterators are sorted (ascending), the result is sorted.
 ///
@@ -62,30 +52,10 @@ where
 ///
 /// See [`.merge_by()`](crate::Itertools::merge_by) for more information.
 #[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
-pub struct MergeBy<I, J, F>
-where
-    I: Iterator,
-    J: Iterator<Item = I::Item>,
-{
-    a: Peekable<I>,
-    b: Peekable<J>,
-    fused: Option<bool>,
-    cmp: F,
-}
-
-impl<I, J, F> fmt::Debug for MergeBy<I, J, F>
-where
-    I: Iterator + fmt::Debug,
-    J: Iterator<Item = I::Item> + fmt::Debug,
-    I::Item: fmt::Debug,
-{
-    debug_fmt_fields!(MergeBy, a, b);
-}
-
-impl<T, F: FnMut(&T, &T) -> bool> MergePredicate<T> for F {
-    fn merge_pred(&mut self, a: &T, b: &T) -> bool {
-        self(a, b)
-    }
+pub struct MergeBy<I: Iterator, J: Iterator, F> {
+    left: PutBack<Fuse<I>>,
+    right: PutBack<Fuse<J>>,
+    cmp_fn: F,
 }
 
 /// Create a `MergeBy` iterator.
@@ -93,72 +63,14 @@ pub fn merge_by_new<I, J, F>(a: I, b: J, cmp: F) -> MergeBy<I::IntoIter, J::Into
 where
     I: IntoIterator,
     J: IntoIterator<Item = I::Item>,
-    F: MergePredicate<I::Item>,
 {
     MergeBy {
-        a: a.into_iter().peekable(),
-        b: b.into_iter().peekable(),
-        fused: None,
-        cmp,
+        left: put_back(a.into_iter().fuse()),
+        right: put_back(b.into_iter().fuse()),
+        cmp_fn: cmp,
     }
 }
 
-impl<I, J, F> Clone for MergeBy<I, J, F>
-where
-    I: Iterator,
-    J: Iterator<Item = I::Item>,
-    Peekable<I>: Clone,
-    Peekable<J>: Clone,
-    F: Clone,
-{
-    clone_fields!(a, b, fused, cmp);
-}
-
-impl<I, J, F> Iterator for MergeBy<I, J, F>
-where
-    I: Iterator,
-    J: Iterator<Item = I::Item>,
-    F: MergePredicate<I::Item>,
-{
-    type Item = I::Item;
-
-    fn next(&mut self) -> Option<Self::Item> {
-        let less_than = match self.fused {
-            Some(lt) => lt,
-            None => match (self.a.peek(), self.b.peek()) {
-                (Some(a), Some(b)) => self.cmp.merge_pred(a, b),
-                (Some(_), None) => {
-                    self.fused = Some(true);
-                    true
-                }
-                (None, Some(_)) => {
-                    self.fused = Some(false);
-                    false
-                }
-                (None, None) => return None,
-            },
-        };
-        if less_than {
-            self.a.next()
-        } else {
-            self.b.next()
-        }
-    }
-
-    fn size_hint(&self) -> (usize, Option<usize>) {
-        // Not ExactSizeIterator because size may be larger than usize
-        size_hint::add(self.a.size_hint(), self.b.size_hint())
-    }
-}
-
-impl<I, J, F> FusedIterator for MergeBy<I, J, F>
-where
-    I: FusedIterator,
-    J: FusedIterator<Item = I::Item>,
-    F: MergePredicate<I::Item>,
-{
-}
-
 /// Return an iterator adaptor that merge-joins items from the two base iterators in ascending order.
 ///
 /// [`IntoIterator`] enabled version of [`Itertools::merge_join_by`].
@@ -171,23 +83,29 @@ where
     I: IntoIterator,
     J: IntoIterator,
     F: FnMut(&I::Item, &J::Item) -> T,
-    T: OrderingOrBool<I::Item, J::Item>,
 {
-    MergeJoinBy {
+    MergeBy {
         left: put_back(left.into_iter().fuse()),
         right: put_back(right.into_iter().fuse()),
-        cmp_fn,
+        cmp_fn: MergeFuncLR(cmp_fn, PhantomData),
     }
 }
 
 /// An iterator adaptor that merge-joins items from the two base iterators in ascending order.
 ///
 /// See [`.merge_join_by()`](crate::Itertools::merge_join_by) for more information.
-#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
-pub struct MergeJoinBy<I: Iterator, J: Iterator, F> {
-    left: PutBack<Fuse<I>>,
-    right: PutBack<Fuse<J>>,
-    cmp_fn: F,
+pub type MergeJoinBy<I, J, F> =
+    MergeBy<I, J, MergeFuncLR<F, <F as FuncLR<<I as Iterator>::Item, <J as Iterator>::Item>>::T>>;
+
+#[derive(Clone, Debug)]
+pub struct MergeFuncLR<F, T>(F, PhantomData<T>);
+
+pub trait FuncLR<L, R> {
+    type T;
+}
+
+impl<L, R, T, F: FnMut(&L, &R) -> T> FuncLR<L, R> for F {
+    type T = T;
 }
 
 pub trait OrderingOrBool<L, R> {
@@ -197,11 +115,11 @@ pub trait OrderingOrBool<L, R> {
     // "merge" never returns (Some(...), Some(...), ...) so Option<Either<I::Item, J::Item>>
     // is appealing but it is always followed by two put_backs, so we think the compiler is
     // smart enough to optimize it. Or we could move put_backs into "merge".
-    fn merge(self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult);
+    fn merge(&mut self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult);
     fn size_hint(left: SizeHint, right: SizeHint) -> SizeHint;
 }
 
-impl<L, R> OrderingOrBool<L, R> for Ordering {
+impl<L, R, F: FnMut(&L, &R) -> Ordering> OrderingOrBool<L, R> for MergeFuncLR<F, Ordering> {
     type MergeResult = EitherOrBoth<L, R>;
     fn left(left: L) -> Self::MergeResult {
         EitherOrBoth::Left(left)
@@ -209,8 +127,8 @@ impl<L, R> OrderingOrBool<L, R> for Ordering {
     fn right(right: R) -> Self::MergeResult {
         EitherOrBoth::Right(right)
     }
-    fn merge(self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult) {
-        match self {
+    fn merge(&mut self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult) {
+        match self.0(&left, &right) {
             Ordering::Equal => (None, None, EitherOrBoth::Both(left, right)),
             Ordering::Less => (None, Some(right), EitherOrBoth::Left(left)),
             Ordering::Greater => (Some(left), None, EitherOrBoth::Right(right)),
@@ -228,7 +146,7 @@ impl<L, R> OrderingOrBool<L, R> for Ordering {
     }
 }
 
-impl<L, R> OrderingOrBool<L, R> for bool {
+impl<L, R, F: FnMut(&L, &R) -> bool> OrderingOrBool<L, R> for MergeFuncLR<F, bool> {
     type MergeResult = Either<L, R>;
     fn left(left: L) -> Self::MergeResult {
         Either::Left(left)
@@ -236,8 +154,8 @@ impl<L, R> OrderingOrBool<L, R> for bool {
     fn right(right: R) -> Self::MergeResult {
         Either::Right(right)
     }
-    fn merge(self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult) {
-        if self {
+    fn merge(&mut self, left: L, right: R) -> (Option<L>, Option<R>, Self::MergeResult) {
+        if self.0(&left, &right) {
             (None, Some(right), Either::Left(left))
         } else {
             (Some(left), None, Either::Right(right))
@@ -249,7 +167,49 @@ impl<L, R> OrderingOrBool<L, R> for bool {
     }
 }
 
-impl<I, J, F> Clone for MergeJoinBy<I, J, F>
+impl<T, F: FnMut(&T, &T) -> bool> OrderingOrBool<T, T> for F {
+    type MergeResult = T;
+    fn left(left: T) -> Self::MergeResult {
+        left
+    }
+    fn right(right: T) -> Self::MergeResult {
+        right
+    }
+    fn merge(&mut self, left: T, right: T) -> (Option<T>, Option<T>, Self::MergeResult) {
+        if self(&left, &right) {
+            (None, Some(right), left)
+        } else {
+            (Some(left), None, right)
+        }
+    }
+    fn size_hint(left: SizeHint, right: SizeHint) -> SizeHint {
+        // Not ExactSizeIterator because size may be larger than usize
+        size_hint::add(left, right)
+    }
+}
+
+impl<T: PartialOrd> OrderingOrBool<T, T> for MergeLte {
+    type MergeResult = T;
+    fn left(left: T) -> Self::MergeResult {
+        left
+    }
+    fn right(right: T) -> Self::MergeResult {
+        right
+    }
+    fn merge(&mut self, left: T, right: T) -> (Option<T>, Option<T>, Self::MergeResult) {
+        if left <= right {
+            (None, Some(right), left)
+        } else {
+            (Some(left), None, right)
+        }
+    }
+    fn size_hint(left: SizeHint, right: SizeHint) -> SizeHint {
+        // Not ExactSizeIterator because size may be larger than usize
+        size_hint::add(left, right)
+    }
+}
+
+impl<I, J, F> Clone for MergeBy<I, J, F>
 where
     I: Iterator,
     J: Iterator,
@@ -260,32 +220,31 @@ where
     clone_fields!(left, right, cmp_fn);
 }
 
-impl<I, J, F> fmt::Debug for MergeJoinBy<I, J, F>
+impl<I, J, F> fmt::Debug for MergeBy<I, J, F>
 where
     I: Iterator + fmt::Debug,
     I::Item: fmt::Debug,
     J: Iterator + fmt::Debug,
     J::Item: fmt::Debug,
 {
-    debug_fmt_fields!(MergeJoinBy, left, right);
+    debug_fmt_fields!(MergeBy, left, right);
 }
 
-impl<I, J, F, T> Iterator for MergeJoinBy<I, J, F>
+impl<I, J, F> Iterator for MergeBy<I, J, F>
 where
     I: Iterator,
     J: Iterator,
-    F: FnMut(&I::Item, &J::Item) -> T,
-    T: OrderingOrBool<I::Item, J::Item>,
+    F: OrderingOrBool<I::Item, J::Item>,
 {
-    type Item = T::MergeResult;
+    type Item = F::MergeResult;
 
     fn next(&mut self) -> Option<Self::Item> {
         match (self.left.next(), self.right.next()) {
             (None, None) => None,
-            (Some(left), None) => Some(T::left(left)),
-            (None, Some(right)) => Some(T::right(right)),
+            (Some(left), None) => Some(F::left(left)),
+            (None, Some(right)) => Some(F::right(right)),
             (Some(left), Some(right)) => {
-                let (left, right, next) = (self.cmp_fn)(&left, &right).merge(left, right);
+                let (left, right, next) = self.cmp_fn.merge(left, right);
                 if let Some(left) = left {
                     self.left.put_back(left);
                 }
@@ -298,7 +257,7 @@ where
     }
 
     fn size_hint(&self) -> SizeHint {
-        T::size_hint(self.left.size_hint(), self.right.size_hint())
+        F::size_hint(self.left.size_hint(), self.right.size_hint())
     }
 
     fn count(mut self) -> usize {
@@ -310,7 +269,7 @@ where
                 (None, Some(_right)) => break count + 1 + self.right.into_parts().1.count(),
                 (Some(left), Some(right)) => {
                     count += 1;
-                    let (left, right, _) = (self.cmp_fn)(&left, &right).merge(left, right);
+                    let (left, right, _) = self.cmp_fn.merge(left, right);
                     if let Some(left) = left {
                         self.left.put_back(left);
                     }
@@ -328,13 +287,13 @@ where
             match (self.left.next(), self.right.next()) {
                 (None, None) => break previous_element,
                 (Some(left), None) => {
-                    break Some(T::left(self.left.into_parts().1.last().unwrap_or(left)))
+                    break Some(F::left(self.left.into_parts().1.last().unwrap_or(left)))
                 }
                 (None, Some(right)) => {
-                    break Some(T::right(self.right.into_parts().1.last().unwrap_or(right)))
+                    break Some(F::right(self.right.into_parts().1.last().unwrap_or(right)))
                 }
                 (Some(left), Some(right)) => {
-                    let (left, right, elem) = (self.cmp_fn)(&left, &right).merge(left, right);
+                    let (left, right, elem) = self.cmp_fn.merge(left, right);
                     if let Some(left) = left {
                         self.left.put_back(left);
                     }
@@ -355,10 +314,10 @@ where
             n -= 1;
             match (self.left.next(), self.right.next()) {
                 (None, None) => break None,
-                (Some(_left), None) => break self.left.nth(n).map(T::left),
-                (None, Some(_right)) => break self.right.nth(n).map(T::right),
+                (Some(_left), None) => break self.left.nth(n).map(F::left),
+                (None, Some(_right)) => break self.right.nth(n).map(F::right),
                 (Some(left), Some(right)) => {
-                    let (left, right, _) = (self.cmp_fn)(&left, &right).merge(left, right);
+                    let (left, right, _) = self.cmp_fn.merge(left, right);
                     if let Some(left) = left {
                         self.left.put_back(left);
                     }
@@ -370,3 +329,11 @@ where
         }
     }
 }
+
+impl<I, J, F> FusedIterator for MergeBy<I, J, F>
+where
+    I: Iterator,
+    J: Iterator,
+    F: OrderingOrBool<I::Item, J::Item>,
+{
+}