diff --git a/library/alloc/src/collections/btree/map.rs b/library/alloc/src/collections/btree/map.rs
index d8421d3c3f70a..7b8417c2758ec 100644
--- a/library/alloc/src/collections/btree/map.rs
+++ b/library/alloc/src/collections/btree/map.rs
@@ -205,7 +205,11 @@ pub struct BTreeMap<
 #[stable(feature = "btree_drop", since = "1.7.0")]
 unsafe impl<#[may_dangle] K, #[may_dangle] V, A: Allocator + Clone> Drop for BTreeMap<K, V, A> {
     fn drop(&mut self) {
-        drop(unsafe { ptr::read(self) }.into_iter())
+        if self.root.is_some() {
+            drop(unsafe { ptr::read(self) }.into_iter())
+        } else {
+            unsafe { ManuallyDrop::drop(&mut self.alloc) }
+        }
     }
 }
 
diff --git a/tests/codegen-llvm/btree-empty-drop.rs b/tests/codegen-llvm/btree-empty-drop.rs
new file mode 100644
index 0000000000000..4e08920f55dbf
--- /dev/null
+++ b/tests/codegen-llvm/btree-empty-drop.rs
@@ -0,0 +1,15 @@
+// Regression test for https://github.com/rust-lang/rust/issues/161375
+// Checking that an empty BTree's drop is optimized away.
+//@ compile-flags: -Copt-level=3
+
+#![crate_type = "lib"]
+
+use std::collections::BTreeMap;
+
+// CHECK-LABEL: @drop_btree
+// CHECK-NOT: dying_next
+// CHECK: ret void
+#[no_mangle]
+pub fn drop_btree() {
+    let _ = BTreeMap::<(), ()>::new();
+}