diff --git a/clippy_lints/src/missing_const_for_fn.rs b/clippy_lints/src/missing_const_for_fn.rs
index bad9e0be82e61..ecc9acf4445d0 100644
--- a/clippy_lints/src/missing_const_for_fn.rs
+++ b/clippy_lints/src/missing_const_for_fn.rs
@@ -3,6 +3,7 @@ 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, meets_msrv, msrvs, trait_ref_of_method};
 use rustc_hir as hir;
+use rustc_hir::def_id::CRATE_DEF_ID;
 use rustc_hir::intravisit::FnKind;
 use rustc_hir::{Body, Constness, FnDecl, GenericParamKind, HirId};
 use rustc_lint::{LateContext, LateLintPass};
@@ -131,6 +132,18 @@ impl<'tcx> LateLintPass<'tcx> for MissingConstForFn {
             FnKind::Closure => return,
         }
 
+        // Const fns are not allowed as methods in a trait.
+        {
+            let parent = cx.tcx.hir().get_parent_item(hir_id);
+            if parent != CRATE_DEF_ID {
+                if let hir::Node::Item(item) = cx.tcx.hir().get_by_def_id(parent) {
+                    if let hir::ItemKind::Trait(..) = &item.kind {
+                        return;
+                    }
+                }
+            }
+        }
+
         let mir = cx.tcx.optimized_mir(def_id);
 
         if let Err((span, err)) = is_min_const_fn(cx.tcx, mir, self.msrv.as_ref()) {
diff --git a/clippy_utils/src/qualify_min_const_fn.rs b/clippy_utils/src/qualify_min_const_fn.rs
index c039fec955db9..891531951c1a0 100644
--- a/clippy_utils/src/qualify_min_const_fn.rs
+++ b/clippy_utils/src/qualify_min_const_fn.rs
@@ -32,32 +32,12 @@ pub fn is_min_const_fn<'a, 'tcx>(tcx: TyCtxt<'tcx>, body: &'a Body<'tcx>, msrv:
                 | ty::PredicateKind::Projection(_)
                 | ty::PredicateKind::ConstEvaluatable(..)
                 | ty::PredicateKind::ConstEquate(..)
+                | ty::PredicateKind::Trait(..)
                 | ty::PredicateKind::TypeWellFormedFromEnv(..) => continue,
                 ty::PredicateKind::ObjectSafe(_) => panic!("object safe predicate on function: {:#?}", predicate),
                 ty::PredicateKind::ClosureKind(..) => panic!("closure kind predicate on function: {:#?}", predicate),
                 ty::PredicateKind::Subtype(_) => panic!("subtype predicate on function: {:#?}", predicate),
                 ty::PredicateKind::Coerce(_) => panic!("coerce predicate on function: {:#?}", predicate),
-                ty::PredicateKind::Trait(pred) => {
-                    if Some(pred.def_id()) == tcx.lang_items().sized_trait() {
-                        continue;
-                    }
-                    match pred.self_ty().kind() {
-                        ty::Param(ref p) => {
-                            let generics = tcx.generics_of(current);
-                            let def = generics.type_param(p, tcx);
-                            let span = tcx.def_span(def.def_id);
-                            return Err((
-                                span,
-                                "trait bounds other than `Sized` \
-                                 on const fn parameters are unstable"
-                                    .into(),
-                            ));
-                        },
-                        // other kinds of bounds are either tautologies
-                        // or cause errors in other passes
-                        _ => continue,
-                    }
-                },
             }
         }
         match predicates.parent {
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 baa7eec05462e..88f6935d224ae 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.rs
+++ b/tests/ui/missing_const_for_fn/could_be_const.rs
@@ -49,8 +49,6 @@ fn sub(x: u32) -> usize {
     unsafe { transmute(&x) }
 }
 
-// NOTE: This is currently not yet allowed to be const
-// Once implemented, Clippy should be able to suggest this as const, too.
 fn generic_arr<T: Copy>(t: [T; 1]) -> T {
     t[0]
 }
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 b89cc6451bb59..3eb52b6827475 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.stderr
+++ b/tests/ui/missing_const_for_fn/could_be_const.stderr
@@ -58,7 +58,15 @@ LL | | }
    | |_^
 
 error: this could be a `const fn`
-  --> $DIR/could_be_const.rs:67:9
+  --> $DIR/could_be_const.rs:52:1
+   |
+LL | / fn generic_arr<T: Copy>(t: [T; 1]) -> T {
+LL | |     t[0]
+LL | | }
+   | |_^
+
+error: this could be a `const fn`
+  --> $DIR/could_be_const.rs:65:9
    |
 LL | /         pub fn b(self, a: &A) -> B {
 LL | |             B
@@ -66,12 +74,12 @@ LL | |         }
    | |_________^
 
 error: this could be a `const fn`
-  --> $DIR/could_be_const.rs:77:5
+  --> $DIR/could_be_const.rs:75:5
    |
 LL | /     fn const_fn_stabilized_before_msrv(byte: u8) {
 LL | |         byte.is_ascii_digit();
 LL | |     }
    | |_____^
 
-error: aborting due to 9 previous errors
+error: aborting due to 10 previous errors