diff --git a/compiler/rustc_codegen_ssa/src/glue.rs b/compiler/rustc_codegen_ssa/src/glue.rs
index 694f5434e9a..e6f402ef19d 100644
--- a/compiler/rustc_codegen_ssa/src/glue.rs
+++ b/compiler/rustc_codegen_ssa/src/glue.rs
@@ -39,7 +39,12 @@ pub fn size_and_align_of_dst<'a, 'tcx, Bx: BuilderMethods<'a, 'tcx>>(
             // The info in this case is the length of the str, so the size is that
             // times the unit size.
             (
-                bx.mul(info.unwrap(), bx.const_usize(unit.size.bytes())),
+                // All slice sizes must fit into `isize`, so this multiplication cannot (signed) wrap.
+                // NOTE: ideally, we want the effects of both `unchecked_smul` and `unchecked_umul`
+                // (resulting in `mul nsw nuw` in LLVM IR), since we know that the multiplication
+                // cannot signed wrap, and that both operands are non-negative. But at the time of writing,
+                // `BuilderMethods` can't do this, and it doesn't seem to enable any further optimizations.
+                bx.unchecked_smul(info.unwrap(), bx.const_usize(unit.size.bytes())),
                 bx.const_usize(unit.align.abi.bytes()),
             )
         }
diff --git a/src/test/codegen/issue-96497-slice-size-nowrap.rs b/src/test/codegen/issue-96497-slice-size-nowrap.rs
new file mode 100644
index 00000000000..a5dbef93460
--- /dev/null
+++ b/src/test/codegen/issue-96497-slice-size-nowrap.rs
@@ -0,0 +1,29 @@
+// This test case checks that LLVM is aware that computing the size of a slice cannot wrap.
+// The possibility of wrapping results in an additional branch when dropping boxed slices
+// in some situations, see https://github.com/rust-lang/rust/issues/96497#issuecomment-1112865218
+
+// compile-flags: -O
+// min-llvm-version: 14.0
+
+#![crate_type="lib"]
+
+// CHECK-LABEL: @simple_size_of_nowrap
+#[no_mangle]
+pub fn simple_size_of_nowrap(x: &[u32]) -> usize {
+    // Make sure the shift used to compute the size has a nowrap flag.
+
+    // CHECK: [[A:%.*]] = shl nsw {{.*}}, 2
+    // CHECK-NEXT: ret {{.*}} [[A]]
+    core::mem::size_of_val(x)
+}
+
+// CHECK-LABEL: @drop_write
+#[no_mangle]
+pub fn drop_write(mut x: Box<[u32]>) {
+    // Check that this write is optimized out.
+    // This depends on the size calculation not wrapping,
+    // since otherwise LLVM can't tell that the memory is always deallocated if the slice len > 0.
+
+    // CHECK-NOT: store i32 42
+    x[1] = 42;
+}