diff --git a/src/term/transform/linearize_matches.rs b/src/term/transform/linearize_matches.rs
index df83d148..7e40664c 100644
--- a/src/term/transform/linearize_matches.rs
+++ b/src/term/transform/linearize_matches.rs
@@ -209,7 +209,9 @@ fn fixed_and_linearized_terms(used_in_arg: HashSet<Name>, bind_terms: Vec<Term>)
 
 /// Get which binds are fixed because they are in the dependency graph
 /// of a free var or of a var used in the match arg.
-fn binds_fixed_by_dependency(mut fixed_binds: HashSet<Name>, bind_terms: &[Term]) -> HashSet<Name> {
+fn binds_fixed_by_dependency(used_in_arg: HashSet<Name>, bind_terms: &[Term]) -> HashSet<Name> {
+  let mut fixed_binds = used_in_arg;
+
   // Find the use dependencies of each bind
   let mut binds = vec![];
   let mut dependency_digraph = HashMap::new();
@@ -275,7 +277,42 @@ fn binds_fixed_by_dependency(mut fixed_binds: HashSet<Name>, bind_terms: &[Term]
       to_visit.extend(deps);
     }
   }
-  used_component
+
+  // Mark lambdas that come before a fixed lambda as also fixed
+  let mut fixed_start = false;
+  let mut fixed_lams = HashSet::new();
+  for term in bind_terms.iter().rev() {
+    if let Term::Lam { pat, .. } = term {
+      if pat.binds().flatten().any(|p| used_component.contains(p)) {
+        fixed_start = true;
+      }
+      if fixed_start {
+        for bind in pat.binds().flatten() {
+          fixed_lams.insert(bind.clone());
+        }
+      }
+    }
+  }
+
+  let mut fixed_binds = used_component;
+
+  // Mark binds that depend on fixed lambdas as also fixed.
+  let mut visited = HashSet::new();
+  let mut to_visit = fixed_lams.iter().collect::<Vec<_>>();
+  while let Some(node) = to_visit.pop() {
+    if visited.contains(node) {
+      continue;
+    }
+    fixed_binds.insert(node.clone());
+    visited.insert(node);
+
+    // Add these dependencies to be checked (if it's not a free var in the match arg)
+    if let Some(deps) = dependency_graph.get(node) {
+      to_visit.extend(deps);
+    }
+  }
+
+  fixed_binds
 }
 
 /* Linearize all used vars */
diff --git a/tests/golden_tests/simplify_matches/complex_with_case.hvm b/tests/golden_tests/simplify_matches/complex_with_case.hvm
new file mode 100644
index 00000000..b926852f
--- /dev/null
+++ b/tests/golden_tests/simplify_matches/complex_with_case.hvm
@@ -0,0 +1,11 @@
+data Tree = (Node lt rt rd ld) | (Leaf val)
+
+(map) =
+  λarg1 λarg2 use tree = arg2;
+  use f = arg1;
+  match tree with f { 
+    Node: (Node (map f tree.lt) (map f tree.rt) (map f tree.rd) (map f tree.ld)); 
+    Leaf: (Leaf (f tree.val)); 
+  }
+
+main = map
\ No newline at end of file
diff --git a/tests/snapshots/simplify_matches__complex_with_case.hvm.snap b/tests/snapshots/simplify_matches__complex_with_case.hvm.snap
new file mode 100644
index 00000000..ca64e130
--- /dev/null
+++ b/tests/snapshots/simplify_matches__complex_with_case.hvm.snap
@@ -0,0 +1,11 @@
+---
+source: tests/golden_tests.rs
+input_file: tests/golden_tests/simplify_matches/complex_with_case.hvm
+---
+(map) = λa λb (match b { Node c d e f: λg (Node (map g c) (map g d) (map g e) (map g f)); Leaf h: λi (Leaf (i h)); } a)
+
+(main) = map
+
+(Node) = λa λb λc λd λe λf (e a b c d)
+
+(Leaf) = λa λb λc (c a)