diff --git a/compiler/rustc_trait_selection/src/traits/misc.rs b/compiler/rustc_trait_selection/src/traits/misc.rs
index cb8f64dd2e8c..2210ef975e6c 100644
--- a/compiler/rustc_trait_selection/src/traits/misc.rs
+++ b/compiler/rustc_trait_selection/src/traits/misc.rs
@@ -93,7 +93,14 @@ pub fn type_allowed_to_implement_const_param_ty<'tcx>(
 ) -> Result<(), ConstParamTyImplementationError<'tcx>> {
     let (adt, substs) = match self_type.kind() {
         // `core` provides these impls.
-        ty::Uint(_) | ty::Int(_) | ty::Bool | ty::Char => return Ok(()),
+        ty::Uint(_)
+        | ty::Int(_)
+        | ty::Bool
+        | ty::Char
+        | ty::Str
+        | ty::Array(..)
+        | ty::Slice(_)
+        | ty::Ref(.., hir::Mutability::Not) => return Ok(()),
 
         &ty::Adt(adt, substs) => (adt, substs),
 
diff --git a/library/core/src/marker.rs b/library/core/src/marker.rs
index 8c240661b2b4..2f9138c56f21 100644
--- a/library/core/src/marker.rs
+++ b/library/core/src/marker.rs
@@ -268,6 +268,7 @@ pub trait StructuralEq {
     // Empty.
 }
 
+// FIXME: Remove special cases of these types from the compiler pattern checking code and always check `T: StructuralEq` instead
 marker_impls! {
     #[unstable(feature = "structural_match", issue = "31434")]
     StructuralEq for
@@ -275,6 +276,10 @@ marker_impls! {
         isize, i8, i16, i32, i64, i128,
         bool,
         char,
+        str /* Technically requires `[u8]: StructuralEq` */,
+        {T: ConstParamTy, const N: usize} [T; N],
+        {T: ConstParamTy} [T],
+        {T: ConstParamTy} &T,
 }
 
 /// Types whose values can be duplicated simply by copying bits.
@@ -988,6 +993,10 @@ marker_impls! {
         isize, i8, i16, i32, i64, i128,
         bool,
         char,
+        str /* Technically requires `[u8]: ConstParamTy` */,
+        {T: ConstParamTy, const N: usize} [T; N],
+        {T: ConstParamTy} [T],
+        {T: ConstParamTy} &T,
 }
 
 /// A common trait implemented by all function pointers.