diff --git a/library/alloc/tests/slice.rs b/library/alloc/tests/slice.rs
index 1fb4a51acfd0a..13b8c059e37ae 100644
--- a/library/alloc/tests/slice.rs
+++ b/library/alloc/tests/slice.rs
@@ -1,6 +1,7 @@
 use std::cell::Cell;
 use std::cmp::Ordering::{self, Equal, Greater, Less};
 use std::convert::identity;
+use std::fmt;
 use std::mem;
 use std::panic;
 use std::rc::Rc;
@@ -993,6 +994,66 @@ fn test_rsplitnator() {
     assert!(xs.rsplitn(0, |x| *x % 2 == 0).next().is_none());
 }
 
+#[test]
+fn test_split_iterators_size_hint() {
+    #[derive(Copy, Clone)]
+    enum Bounds {
+        Lower,
+        Upper,
+    }
+    fn assert_tight_size_hints(mut it: impl Iterator, which: Bounds, ctx: impl fmt::Display) {
+        match which {
+            Bounds::Lower => {
+                let mut lower_bounds = vec![it.size_hint().0];
+                while let Some(_) = it.next() {
+                    lower_bounds.push(it.size_hint().0);
+                }
+                let target: Vec<_> = (0..lower_bounds.len()).rev().collect();
+                assert_eq!(lower_bounds, target, "lower bounds incorrect or not tight: {}", ctx);
+            }
+            Bounds::Upper => {
+                let mut upper_bounds = vec![it.size_hint().1];
+                while let Some(_) = it.next() {
+                    upper_bounds.push(it.size_hint().1);
+                }
+                let target: Vec<_> = (0..upper_bounds.len()).map(Some).rev().collect();
+                assert_eq!(upper_bounds, target, "upper bounds incorrect or not tight: {}", ctx);
+            }
+        }
+    }
+
+    for len in 0..=2 {
+        let mut v: Vec<u8> = (0..len).collect();
+
+        // p: predicate, b: bound selection
+        for (p, b) in [
+            // with a predicate always returning false, the split*-iterators
+            // become maximally short, so the size_hint lower bounds are tight
+            ((|_| false) as fn(&_) -> _, Bounds::Lower),
+            // with a predicate always returning true, the split*-iterators
+            // become maximally long, so the size_hint upper bounds are tight
+            ((|_| true) as fn(&_) -> _, Bounds::Upper),
+        ] {
+            use assert_tight_size_hints as a;
+            use format_args as f;
+
+            a(v.split(p), b, "split");
+            a(v.split_mut(p), b, "split_mut");
+            a(v.split_inclusive(p), b, "split_inclusive");
+            a(v.split_inclusive_mut(p), b, "split_inclusive_mut");
+            a(v.rsplit(p), b, "rsplit");
+            a(v.rsplit_mut(p), b, "rsplit_mut");
+
+            for n in 0..=3 {
+                a(v.splitn(n, p), b, f!("splitn, n = {}", n));
+                a(v.splitn_mut(n, p), b, f!("splitn_mut, n = {}", n));
+                a(v.rsplitn(n, p), b, f!("rsplitn, n = {}", n));
+                a(v.rsplitn_mut(n, p), b, f!("rsplitn_mut, n = {}", n));
+            }
+        }
+    }
+}
+
 #[test]
 fn test_windowsator() {
     let v = &[1, 2, 3, 4];
diff --git a/library/core/src/slice/iter.rs b/library/core/src/slice/iter.rs
index d67af9cf6680c..c0dfba490eca7 100644
--- a/library/core/src/slice/iter.rs
+++ b/library/core/src/slice/iter.rs
@@ -400,7 +400,13 @@ where
 
     #[inline]
     fn size_hint(&self) -> (usize, Option<usize>) {
-        if self.finished { (0, Some(0)) } else { (1, Some(self.v.len() + 1)) }
+        if self.finished {
+            (0, Some(0))
+        } else {
+            // If the predicate doesn't match anything, we yield one slice.
+            // If it matches every element, we yield `len() + 1` empty slices.
+            (1, Some(self.v.len() + 1))
+        }
     }
 }
 
@@ -525,7 +531,14 @@ where
 
     #[inline]
     fn size_hint(&self) -> (usize, Option<usize>) {
-        if self.finished { (0, Some(0)) } else { (1, Some(self.v.len() + 1)) }
+        if self.finished {
+            (0, Some(0))
+        } else {
+            // If the predicate doesn't match anything, we yield one slice.
+            // If it matches every element, we yield `len()` one-element slices,
+            // or a single empty slice.
+            (1, Some(cmp::max(1, self.v.len())))
+        }
     }
 }
 
@@ -647,8 +660,8 @@ where
         if self.finished {
             (0, Some(0))
         } else {
-            // if the predicate doesn't match anything, we yield one slice
-            // if it matches every element, we yield len+1 empty slices.
+            // If the predicate doesn't match anything, we yield one slice.
+            // If it matches every element, we yield `len() + 1` empty slices.
             (1, Some(self.v.len() + 1))
         }
     }
@@ -763,9 +776,10 @@ where
         if self.finished {
             (0, Some(0))
         } else {
-            // if the predicate doesn't match anything, we yield one slice
-            // if it matches every element, we yield len+1 empty slices.
-            (1, Some(self.v.len() + 1))
+            // If the predicate doesn't match anything, we yield one slice.
+            // If it matches every element, we yield `len()` one-element slices,
+            // or a single empty slice.
+            (1, Some(cmp::max(1, self.v.len())))
         }
     }
 }
@@ -1008,7 +1022,10 @@ impl<T, I: SplitIter<Item = T>> Iterator for GenericSplitN<I> {
     #[inline]
     fn size_hint(&self) -> (usize, Option<usize>) {
         let (lower, upper_opt) = self.iter.size_hint();
-        (lower, upper_opt.map(|upper| cmp::min(self.count, upper)))
+        (
+            cmp::min(self.count, lower),
+            Some(upper_opt.map_or(self.count, |upper| cmp::min(self.count, upper))),
+        )
     }
 }