diff --git a/library/alloc/src/vec.rs b/library/alloc/src/vec.rs
index 8ca0a0883cb16..80f7ff4893e21 100644
--- a/library/alloc/src/vec.rs
+++ b/library/alloc/src/vec.rs
@@ -622,7 +622,10 @@ impl<T> Vec<T> {
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn shrink_to_fit(&mut self) {
-        if self.capacity() != self.len {
+        // The capacity is never less than the length, and there's nothing to do when
+        // they are equal, so we can avoid the panic case in `RawVec::shrink_to_fit`
+        // by only calling it with a greater capacity.
+        if self.capacity() > self.len {
             self.buf.shrink_to_fit(self.len);
         }
     }
diff --git a/src/test/codegen/vec-shrink-panic.rs b/src/test/codegen/vec-shrink-panic.rs
new file mode 100644
index 0000000000000..690c7e6d6ced2
--- /dev/null
+++ b/src/test/codegen/vec-shrink-panic.rs
@@ -0,0 +1,36 @@
+// compile-flags: -O
+// ignore-debug: the debug assertions get in the way
+#![crate_type = "lib"]
+#![feature(shrink_to)]
+
+// Make sure that `Vec::shrink_to_fit` never emits panics via `RawVec::shrink_to_fit`,
+// "Tried to shrink to a larger capacity", because the length is *always* <= capacity.
+
+// CHECK-LABEL: @shrink_to_fit
+#[no_mangle]
+pub fn shrink_to_fit(vec: &mut Vec<u32>) {
+    // CHECK-NOT: panic
+    vec.shrink_to_fit();
+}
+
+// CHECK-LABEL: @issue71861
+#[no_mangle]
+pub fn issue71861(n: usize) -> Box<[u32]> {
+    // CHECK-NOT: panic
+    vec![0; n].into_boxed_slice()
+}
+
+// CHECK-LABEL: @issue75636
+#[no_mangle]
+pub fn issue75636<'a>(iter: &[&'a str]) -> Box<[&'a str]> {
+    // CHECK-NOT: panic
+    iter.iter().copied().collect()
+}
+
+// Sanity-check that we do see a possible panic for an arbitrary `Vec::shrink_to`.
+// CHECK-LABEL: @shrink_to
+#[no_mangle]
+pub fn shrink_to(vec: &mut Vec<u32>) {
+    // CHECK: panic
+    vec.shrink_to(42);
+}