diff --git a/src/liballoc/raw_vec.rs b/src/liballoc/raw_vec.rs
index d46bf81f996f7..f348b5b69780b 100644
--- a/src/liballoc/raw_vec.rs
+++ b/src/liballoc/raw_vec.rs
@@ -407,13 +407,34 @@ impl<T, A: AllocRef> RawVec<T, A> {
             return Err(CapacityOverflow);
         }
 
+        if needed_extra_capacity == 0 {
+            return Ok(());
+        }
+
         // Nothing we can really do about these checks, sadly.
         let required_cap =
             used_capacity.checked_add(needed_extra_capacity).ok_or(CapacityOverflow)?;
-        // Cannot overflow, because `cap <= isize::MAX`, and type of `cap` is `usize`.
-        let double_cap = self.cap * 2;
-        // `double_cap` guarantees exponential growth.
-        let cap = cmp::max(double_cap, required_cap);
+
+        // This guarantees exponential growth. The doubling cannot overflow
+        // because `cap <= isize::MAX` and the type of `cap` is `usize`.
+        let cap = cmp::max(self.cap * 2, required_cap);
+
+        // Tiny Vecs are dumb. Skip to:
+        // - 8 if the element size is 1, because any heap allocators is likely
+        //   to round up a request of less than 8 bytes to at least 8 bytes.
+        // - 4 if elements are moderate-sized (<= 1 KiB).
+        // - 1 otherwise, to avoid wasting too much space for very short Vecs.
+        // Note that `min_non_zero_cap` is computed statically.
+        let elem_size = mem::size_of::<T>();
+        let min_non_zero_cap = if elem_size == 1 {
+            8
+        } else if elem_size <= 1024 {
+            4
+        } else {
+            1
+        };
+        let cap = cmp::max(min_non_zero_cap, cap);
+
         let new_layout = Layout::array::<T>(cap);
 
         // `finish_grow` is non-generic over `T`.
diff --git a/src/liballoc/raw_vec/tests.rs b/src/liballoc/raw_vec/tests.rs
index e7ab8a305d279..17622d72a059c 100644
--- a/src/liballoc/raw_vec/tests.rs
+++ b/src/liballoc/raw_vec/tests.rs
@@ -59,7 +59,7 @@ fn reserve_does_not_overallocate() {
         let mut v: RawVec<u32> = RawVec::new();
         v.reserve(0, 7);
         assert_eq!(7, v.capacity());
-        // 97 if more than double of 7, so `reserve` should work
+        // 97 is more than double of 7, so `reserve` should work
         // like `reserve_exact`.
         v.reserve(7, 90);
         assert_eq!(97, v.capacity());
diff --git a/src/liballoc/tests/vec.rs b/src/liballoc/tests/vec.rs
index 3d76324f7e880..b16044d964045 100644
--- a/src/liballoc/tests/vec.rs
+++ b/src/liballoc/tests/vec.rs
@@ -1473,3 +1473,118 @@ fn vec_macro_repeating_null_raw_fat_pointer() {
         vtable: *mut (),
     }
 }
+
+// This test will likely fail if you change the capacities used in
+// `RawVec::grow_amortized`.
+#[test]
+fn test_push_growth_strategy() {
+    // If the element size is 1, we jump from 0 to 8, then double.
+    {
+        let mut v1: Vec<u8> = vec![];
+        assert_eq!(v1.capacity(), 0);
+
+        for _ in 0..8 {
+            v1.push(0);
+            assert_eq!(v1.capacity(), 8);
+        }
+
+        for _ in 8..16 {
+            v1.push(0);
+            assert_eq!(v1.capacity(), 16);
+        }
+
+        for _ in 16..32 {
+            v1.push(0);
+            assert_eq!(v1.capacity(), 32);
+        }
+
+        for _ in 32..64 {
+            v1.push(0);
+            assert_eq!(v1.capacity(), 64);
+        }
+    }
+
+    // If the element size is 2..=1024, we jump from 0 to 4, then double.
+    {
+        let mut v2: Vec<u16> = vec![];
+        let mut v1024: Vec<[u8; 1024]> = vec![];
+        assert_eq!(v2.capacity(), 0);
+        assert_eq!(v1024.capacity(), 0);
+
+        for _ in 0..4 {
+            v2.push(0);
+            v1024.push([0; 1024]);
+            assert_eq!(v2.capacity(), 4);
+            assert_eq!(v1024.capacity(), 4);
+        }
+
+        for _ in 4..8 {
+            v2.push(0);
+            v1024.push([0; 1024]);
+            assert_eq!(v2.capacity(), 8);
+            assert_eq!(v1024.capacity(), 8);
+        }
+
+        for _ in 8..16 {
+            v2.push(0);
+            v1024.push([0; 1024]);
+            assert_eq!(v2.capacity(), 16);
+            assert_eq!(v1024.capacity(), 16);
+        }
+
+        for _ in 16..32 {
+            v2.push(0);
+            v1024.push([0; 1024]);
+            assert_eq!(v2.capacity(), 32);
+            assert_eq!(v1024.capacity(), 32);
+        }
+
+        for _ in 32..64 {
+            v2.push(0);
+            v1024.push([0; 1024]);
+            assert_eq!(v2.capacity(), 64);
+            assert_eq!(v1024.capacity(), 64);
+        }
+    }
+
+    // If the element size is > 1024, we jump from 0 to 1, then double.
+    {
+        let mut v1025: Vec<[u8; 1025]> = vec![];
+        assert_eq!(v1025.capacity(), 0);
+
+        for _ in 0..1 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 1);
+        }
+
+        for _ in 1..2 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 2);
+        }
+
+        for _ in 2..4 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 4);
+        }
+
+        for _ in 4..8 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 8);
+        }
+
+        for _ in 8..16 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 16);
+        }
+
+        for _ in 16..32 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 32);
+        }
+
+        for _ in 32..64 {
+            v1025.push([0; 1025]);
+            assert_eq!(v1025.capacity(), 64);
+        }
+    }
+}