diff --git a/rust/pin-init/examples/selfref.rs b/rust/pin-init/examples/selfref.rs
index 5e9494dcc17e..5212b9255b75 100644
--- a/rust/pin-init/examples/selfref.rs
+++ b/rust/pin-init/examples/selfref.rs
@@ -6,6 +6,9 @@
 
 #[pin_data]
 struct SelfRef {
+    #[uses('_: invariant)]
+    not_cov: Box<dyn Fn(&'str str) -> bool + 'str>,
+
     part: &'str str,
     str: String,
 
@@ -20,6 +23,7 @@ fn use_self_ref() {
         part: &str[..5],
         mut_str: "hello world".to_owned(),
         mut_part: &mut mut_str[..5],
+        not_cov: Box::new(move |s| s == str),
     }));
 
     // Access via projection.
@@ -41,6 +45,14 @@ fn use_self_ref() {
     foo.as_mut().with_project(|proj| {
         proj.mut_part.make_ascii_uppercase();
     });
+
+    // Access non-covariant type using `with_` accessor.
+    foo.with_not_cov(|not_cov| {
+        not_cov("");
+    });
+
+    // Access non-covariant type using `with_project`.
+    foo.as_mut().with_project(|proj| (proj.not_cov)(proj.str));
 }
 
 fn main() {
diff --git a/rust/pin-init/internal/src/pin_data.rs b/rust/pin-init/internal/src/pin_data.rs
index 77c8ce260403..4b361c510a40 100644
--- a/rust/pin-init/internal/src/pin_data.rs
+++ b/rust/pin-init/internal/src/pin_data.rs
@@ -1441,7 +1441,24 @@ fn generate_projections(info: &StructInfo) -> TokenStream {
                 }
             ))
         } else {
-            continue;
+            let f_doc = format!("Access the `{ident}` field on a shared reference of `Self`.");
+            let vis = &f.field.vis;
+            let with_ident = format_ident!("with_{ident}");
+
+            let all_lifetimes: Vec<_> = f.captures.iter().map(|b| &b.lifetime).collect();
+            let ty = &f.field.ty;
+
+            accessors.push(quote!(
+                #[doc = #f_doc]
+                #[inline]
+                #vis fn #with_ident<'__this, R>(
+                    &'__this self,
+                    f: impl for<#(#all_lifetimes,)*> ::core::ops::FnOnce(&'__this #ty) -> R,
+                ) -> R {
+                    // SAFETY: we have `Erase<..>` which we know is layout compatible with `f.ty`.
+                    f(unsafe { ::core::mem::transmute(&self.#member) })
+                }
+            ))
         }
     }