diff --git a/CHANGELOG.md b/CHANGELOG.md
index b0872af6d3..b27a5edb49 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,13 @@ A [separate changelog is kept for rand_core](rand_core/CHANGELOG.md).
 
 You may also find the [Upgrade Guide](https://rust-random.github.io/book/update.html) useful.
 
+## [Unreleased API changing release]
+
+### Other
+- Simpler and faster implementation of Floyd's F2 (#1277). This
+  changes some outputs from `rand::seq::index::sample` and
+  `rand::seq::SliceRandom::choose_multiple`.
+
 ## [0.8.5] - 2021-08-20
 ### Fixes
 - Fix build on non-32/64-bit architectures (#1144)
diff --git a/src/seq/index.rs b/src/seq/index.rs
index ecd7d9f738..b7bc6a9b26 100644
--- a/src/seq/index.rs
+++ b/src/seq/index.rs
@@ -380,33 +380,18 @@ where
 /// This implementation uses `O(amount)` memory and `O(amount^2)` time.
 fn sample_floyd<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
 where R: Rng + ?Sized {
-    // For small amount we use Floyd's fully-shuffled variant. For larger
-    // amounts this is slow due to Vec::insert performance, so we shuffle
-    // afterwards. Benchmarks show little overhead from extra logic.
-    let floyd_shuffle = amount < 50;
-
+    // Note that the values returned by `rng.gen_range()` can be
+    // inferred from the returned vector by working backwards from
+    // the last entry. This bijection proves the algorithm fair.
     debug_assert!(amount <= length);
     let mut indices = Vec::with_capacity(amount as usize);
     for j in length - amount..length {
         let t = rng.gen_range(0..=j);
-        if floyd_shuffle {
-            if let Some(pos) = indices.iter().position(|&x| x == t) {
-                indices.insert(pos, j);
-                continue;
-            }
-        } else if indices.contains(&t) {
-            indices.push(j);
-            continue;
+        if let Some(pos) = indices.iter().position(|&x| x == t) {
+            indices[pos] = j;
         }
         indices.push(t);
     }
-    if !floyd_shuffle {
-        // Reimplement SliceRandom::shuffle with smaller indices
-        for i in (1..amount).rev() {
-            // invariant: elements with index > i have been locked in place.
-            indices.swap(i as usize, rng.gen_range(0..=i) as usize);
-        }
-    }
     IndexVec::from(indices)
 }
 
@@ -628,8 +613,8 @@ mod test {
             );
         };
 
-        do_test(10, 6, &[8, 0, 3, 5, 9, 6]); // floyd
-        do_test(25, 10, &[18, 15, 14, 9, 0, 13, 5, 24]); // floyd
+        do_test(10, 6, &[8, 3, 5, 9, 0, 6]); // floyd
+        do_test(25, 10, &[18, 14, 9, 15, 0, 13, 5, 24]); // floyd
         do_test(300, 8, &[30, 283, 150, 1, 73, 13, 285, 35]); // floyd
         do_test(300, 80, &[31, 289, 248, 154, 5, 78, 19, 286]); // inplace
         do_test(300, 180, &[31, 289, 248, 154, 5, 78, 19, 286]); // inplace
diff --git a/src/seq/mod.rs b/src/seq/mod.rs
index 24c65bc9f0..a61e516924 100644
--- a/src/seq/mod.rs
+++ b/src/seq/mod.rs
@@ -725,7 +725,7 @@ mod test {
                 .choose_multiple(&mut r, 8)
                 .cloned()
                 .collect::<Vec<char>>(),
-            &['d', 'm', 'b', 'n', 'c', 'k', 'h', 'e']
+            &['d', 'm', 'n', 'k', 'h', 'e', 'b', 'c']
         );
 
         #[cfg(feature = "alloc")]