diff --git a/clippy_lints/src/missing_const_for_fn.rs b/clippy_lints/src/missing_const_for_fn.rs
index 9ba19e0a865..4592324809f 100644
--- a/clippy_lints/src/missing_const_for_fn.rs
+++ b/clippy_lints/src/missing_const_for_fn.rs
@@ -1,7 +1,6 @@
 use clippy_config::msrvs::{self, Msrv};
 use clippy_utils::diagnostics::span_lint;
 use clippy_utils::qualify_min_const_fn::is_min_const_fn;
-use clippy_utils::ty::has_drop;
 use clippy_utils::{fn_has_unsatisfiable_preds, is_entrypoint_fn, is_from_proc_macro, trait_ref_of_method};
 use rustc_hir as hir;
 use rustc_hir::def_id::CRATE_DEF_ID;
@@ -121,10 +120,7 @@ fn check_fn(
                 }
             },
             FnKind::Method(_, sig, ..) => {
-                if trait_ref_of_method(cx, def_id).is_some()
-                    || already_const(sig.header)
-                    || method_accepts_droppable(cx, def_id)
-                {
+                if trait_ref_of_method(cx, def_id).is_some() || already_const(sig.header) {
                     return;
                 }
             },
@@ -151,26 +147,13 @@ fn check_fn(
 
         let mir = cx.tcx.optimized_mir(def_id);
 
-        if let Err((span, err)) = is_min_const_fn(cx.tcx, mir, &self.msrv) {
-            if cx.tcx.is_const_fn_raw(def_id.to_def_id()) {
-                cx.tcx.dcx().span_err(span, err);
-            }
-        } else {
+        if let Ok(()) = is_min_const_fn(cx.tcx, mir, &self.msrv) {
             span_lint(cx, MISSING_CONST_FOR_FN, span, "this could be a `const fn`");
         }
     }
     extract_msrv_attr!(LateContext);
 }
 
-/// Returns true if any of the method parameters is a type that implements `Drop`. The method
-/// can't be made const then, because `drop` can't be const-evaluated.
-fn method_accepts_droppable(cx: &LateContext<'_>, def_id: LocalDefId) -> bool {
-    let sig = cx.tcx.fn_sig(def_id).instantiate_identity().skip_binder();
-
-    // If any of the params are droppable, return true
-    sig.inputs().iter().any(|&ty| has_drop(cx, ty))
-}
-
 // We don't have to lint on something that's already `const`
 #[must_use]
 fn already_const(header: hir::FnHeader) -> bool {
diff --git a/clippy_utils/src/qualify_min_const_fn.rs b/clippy_utils/src/qualify_min_const_fn.rs
index 81e94725a70..42b10f69c0c 100644
--- a/clippy_utils/src/qualify_min_const_fn.rs
+++ b/clippy_utils/src/qualify_min_const_fn.rs
@@ -40,9 +40,13 @@ pub fn is_min_const_fn<'tcx>(tcx: TyCtxt<'tcx>, body: &Body<'tcx>, msrv: &Msrv)
     )?;
 
     for bb in &*body.basic_blocks {
-        check_terminator(tcx, body, bb.terminator(), msrv)?;
-        for stmt in &bb.statements {
-            check_statement(tcx, body, def_id, stmt, msrv)?;
+        // Cleanup blocks are ignored entirely by const eval, so we can too:
+        // https://github.com/rust-lang/rust/blob/1dea922ea6e74f99a0e97de5cdb8174e4dea0444/compiler/rustc_const_eval/src/transform/check_consts/check.rs#L382
+        if !bb.is_cleanup {
+            check_terminator(tcx, body, bb.terminator(), msrv)?;
+            for stmt in &bb.statements {
+                check_statement(tcx, body, def_id, stmt, msrv)?;
+            }
         }
     }
     Ok(())
diff --git a/tests/ui/missing_const_for_fn/could_be_const.rs b/tests/ui/missing_const_for_fn/could_be_const.rs
index 06dbbeb31c0..58e639cc7fd 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.rs
+++ b/tests/ui/missing_const_for_fn/could_be_const.rs
@@ -141,3 +141,33 @@ fn union_access_can_be_const() {
         let _ = unsafe { bar.val };
     }
 }
+
+mod issue12677 {
+    pub struct Wrapper {
+        pub strings: Vec<String>,
+    }
+
+    impl Wrapper {
+        #[must_use]
+        pub fn new(strings: Vec<String>) -> Self {
+            Self { strings }
+        }
+
+        #[must_use]
+        pub fn empty() -> Self {
+            Self { strings: Vec::new() }
+        }
+    }
+
+    pub struct Other {
+        pub text: String,
+        pub vec: Vec<String>,
+    }
+
+    impl Other {
+        pub fn new(text: String) -> Self {
+            let vec = Vec::new();
+            Self { text, vec }
+        }
+    }
+}
diff --git a/tests/ui/missing_const_for_fn/could_be_const.stderr b/tests/ui/missing_const_for_fn/could_be_const.stderr
index b2cade30563..1c61c3e8713 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.stderr
+++ b/tests/ui/missing_const_for_fn/could_be_const.stderr
@@ -130,5 +130,30 @@ LL | |         let _ = unsafe { bar.val };
 LL | |     }
    | |_____^
 
-error: aborting due to 14 previous errors
+error: this could be a `const fn`
+  --> tests/ui/missing_const_for_fn/could_be_const.rs:152:9
+   |
+LL | /         pub fn new(strings: Vec<String>) -> Self {
+LL | |             Self { strings }
+LL | |         }
+   | |_________^
+
+error: this could be a `const fn`
+  --> tests/ui/missing_const_for_fn/could_be_const.rs:157:9
+   |
+LL | /         pub fn empty() -> Self {
+LL | |             Self { strings: Vec::new() }
+LL | |         }
+   | |_________^
+
+error: this could be a `const fn`
+  --> tests/ui/missing_const_for_fn/could_be_const.rs:168:9
+   |
+LL | /         pub fn new(text: String) -> Self {
+LL | |             let vec = Vec::new();
+LL | |             Self { text, vec }
+LL | |         }
+   | |_________^
+
+error: aborting due to 17 previous errors