diff --git a/src/types/mod.rs b/src/types/mod.rs
index 0189c12..209107a 100644
--- a/src/types/mod.rs
+++ b/src/types/mod.rs
@@ -1752,6 +1752,8 @@ pub struct Hole {
     /// more arguments) unifies with the hole's type — shown applied to further holes
     /// (`String.upper ?`, `String.concat ? ?`). Fewest-holes-first, capped.
     pub refinements: Vec<String>,
+    /// How many further refinement fits the cap left out of `refinements`.
+    pub more_refinements: usize,
     pub span: Span,
 }
 
@@ -1771,7 +1773,11 @@ impl Hole {
             parts.push(format!("try: {}{more}", self.fits.join(", ")));
         }
         if !self.refinements.is_empty() {
-            parts.push(format!("or: {}", self.refinements.join(", ")));
+            let more = match self.more_refinements {
+                0 => String::new(),
+                n => format!(", and {n} more"),
+            };
+            parts.push(format!("or: {}{more}", self.refinements.join(", ")));
         }
         parts.join(" — ")
     }
@@ -2458,13 +2464,15 @@ fn run(module: &Module, record: bool, imports: &HashMap<String, ModuleExports>)
         .map(|(span, name, ty, env)| {
             let (fits, more_fits) = inf.hole_fits(&env, &ty, name.as_deref());
             let direct: std::collections::HashSet<String> = fits.iter().cloned().collect();
-            let refinements = inf.hole_refinements(&env, &ty, &direct, name.as_deref());
+            let (refinements, more_refinements) =
+                inf.hole_refinements(&env, &ty, &direct, name.as_deref());
             Hole {
                 name,
                 ty: show(&inf.apply(&ty)),
                 fits,
                 more_fits,
                 refinements,
+                more_refinements,
                 span,
             }
         })
@@ -9576,16 +9584,17 @@ impl Infer {
     /// keeps out trivially-general combinators (`id`, `const`) that would otherwise
     /// "refine" into every hole. `direct` is the set already reported as direct fits.
     /// Fewest-holes-first, then fewest generalized vars, then unqualified, then name.
+    /// Returns the shortlist and how many further refinements the cap left out.
     fn hole_refinements(
         &mut self,
         env: &Env,
         target: &Ty,
         direct: &std::collections::HashSet<String>,
         hole: Option<&str>,
-    ) -> Vec<String> {
+    ) -> (Vec<String>, usize) {
         let target = self.apply(target);
         if matches!(target, Ty::Var(_)) {
-            return Vec::new();
+            return (Vec::new(), 0);
         }
         let snap = self.subst_snapshot();
         let mut out: Vec<(u8, usize, usize, bool, usize, String)> = Vec::new();
@@ -9633,10 +9642,13 @@ impl Infer {
             }
         }
         out.sort();
-        out.into_iter()
+        let more = out.len().saturating_sub(REFINE_CAP);
+        let shown = out
+            .into_iter()
             .map(|(_, _, _, _, _, s)| s)
             .take(REFINE_CAP)
-            .collect()
+            .collect();
+        (shown, more)
     }
 
     fn instantiate(&mut self, scheme: &Scheme) -> Ty {
diff --git a/tests/typecheck.rs b/tests/typecheck.rs
index 3f9cceb..48c7d22 100644
--- a/tests/typecheck.rs
+++ b/tests/typecheck.rs
@@ -3928,6 +3928,36 @@ fn a_truncated_fit_list_says_how_many_it_left_out() {
     );
 }
 
+#[test]
+fn a_truncated_refinement_list_says_how_many_it_left_out() {
+    // Same string->string hole as the truncated direct-fit case: many functions
+    // refine into it (String.lower ?, String.upper ?, …), so the refinement
+    // shortlist is capped and must say how many it left out.
+    let module =
+        pyfun::parse("let r = [\"a\"] |> List.map ?f |> String.join \",\"").expect("parse");
+    let (_e, _t, holes, _ordered, _codecs) = pyfun::types::check_collecting(&module);
+    let hole = &holes[0];
+    assert_eq!(hole.refinements.len(), 4);
+    assert!(hole.more_refinements > 0);
+    // The "and N more" for refinements sits on the `or:` clause; pin that the
+    // message reports the leftover count (the try: clause also has one for fits).
+    assert!(
+        hole.message()
+            .contains(&format!("or: {}", hole.refinements.join(", "))),
+        "{}",
+        hole.message()
+    );
+    assert!(
+        hole.message().contains(&format!(
+            "or: {}, and {} more",
+            hole.refinements.join(", "),
+            hole.more_refinements
+        )),
+        "{}",
+        hole.message()
+    );
+}
+
 #[test]
 fn an_unconstrained_hole_lists_no_fits() {
     // A bare, fully-polymorphic hole (`'a`) would match everything — unhelpful, so