diff --git a/documentation/source/release-notes/2024.2.rst b/documentation/source/release-notes/2024.2.rst
index 2d7715a16..258fb9f6a 100644
--- a/documentation/source/release-notes/2024.2.rst
+++ b/documentation/source/release-notes/2024.2.rst
@@ -26,6 +26,19 @@ Compiler
 * The build rules for unified executables now properly depend on
   copying included run-time libraries such as libunwind.
 
+* Optimizations that allow the type of ``if`` expressions to be more
+  accurately estimated have been improved. For example, in this
+  function:
+
+  .. code-block::
+
+    define function if-example (arg :: false-or(<integer>)) => (result :: <integer>);
+      min(arg | 20, 30)
+    end;
+
+  the comparison can now be properly inlined because the first
+  argument to :drm:`min` is known to be an :drm:`<integer>`.
+
 Tools
 =====
 
diff --git a/sources/dfmc/optimization/assignment.dylan b/sources/dfmc/optimization/assignment.dylan
index 254833bff..af2b44503 100644
--- a/sources/dfmc/optimization/assignment.dylan
+++ b/sources/dfmc/optimization/assignment.dylan
@@ -190,14 +190,20 @@ define method maybe-rename-temporaries-in-conditional
           (c.environment, <constrain-type>,
            value: to-be-renamed, type: constraint);
       let then-f = c.consequent;
+      let merge-c :: <if-merge> = c.next-computation;
       let changed? = #f;
       rename-temporary!(to-be-renamed, tt-t);
-      for-computations(tc from then-f before c.next-computation)
+      for-computations(tc from then-f before merge-c)
         let now-changed? = rename-temporary-references!(tc, to-be-renamed, tt-t);
         changed? := (changed? | now-changed?);
       end;
+      // The left side of the merge is also part of the consequent
+      if (merge-c.merge-left-value == to-be-renamed)
+        merge-replace-left-value!(merge-c, to-be-renamed, tt-t);
+        changed? := #t;
+      end;
       if (changed?)
-        insert-computation-before!(then-f, tt-c);
+        insert-computation-before-reference!(then-f, tt-c, tt-t);
       else // It's not used in the consequent, so get rid of it.
         remove-user!(to-be-renamed, tt-c);
       end;
diff --git a/sources/dfmc/optimization/calls.dylan b/sources/dfmc/optimization/calls.dylan
index 3ad03bfd2..9f53b3910 100644
--- a/sources/dfmc/optimization/calls.dylan
+++ b/sources/dfmc/optimization/calls.dylan
@@ -79,13 +79,19 @@ define method do-optimize-instance?-user(c :: <if>, object, type) => ();
     = make-with-temporary(c.environment, <constrain-type>,
                           value: object, type: type);
   let then-f = c.consequent;
+  let merge-c :: <if-merge> = c.next-computation;
   let changed? = #f;
-  for-computations(tc from then-f before c.next-computation)
+  for-computations(tc from then-f before merge-c)
     let now-changed? = rename-temporary-references!(tc, object, tt-t);
     changed? := (changed? | now-changed?);
   end;
+  // The left side of the merge is also part of the consequent
+  if (merge-c.merge-left-value == object)
+    merge-replace-left-value!(merge-c, object, tt-t);
+    changed? := #t;
+  end;
   if (changed?)
-    insert-computation-before!(then-f, tt-c);
+    insert-computation-before-reference!(then-f, tt-c, tt-t);
   else // It's not used in the consequent, so get rid of it.
     remove-user!(object, tt-c);
   end