diff --git a/pkgs/racket-test-core/tests/racket/optimize.rktl b/pkgs/racket-test-core/tests/racket/optimize.rktl
index 1409fc586f..595dc2888c 100644
--- a/pkgs/racket-test-core/tests/racket/optimize.rktl
+++ b/pkgs/racket-test-core/tests/racket/optimize.rktl
@@ -1093,7 +1093,32 @@
                     `(letrec ([x (,e? y y)]
                               [y (random)])
                        (list x x y y))
-                    #f))])
+                    #f)
+         (test-comp `(lambda (x y) (when (and (pair? x) (box? y)) (,e? x y)))
+                    `(lambda (x y) (when (and (pair? x) (box? y)) #f)))
+         (test-comp `(lambda (x y) (car x) (unbox y) (,e? x y))
+                    `(lambda (x y) (car x) (unbox y) #f))
+         (test-comp `(lambda (x) (car x) (,e? x (box 0)))
+                    `(lambda (x) (car x) #f))
+         ;Ensure that the reduction doesn't eliminate side effects
+         (test-comp `(lambda (x) (car x) (,e? (begin (newline) x) (box 0)))
+                    `(lambda (x) (car x) #f)
+                    #f)
+         (test-comp `(lambda (x) (car x) (,e? x (begin (newline) (box 0))))
+                    `(lambda (x) (car x) #f)
+                    #f)
+         (test-comp `(lambda () (,e? (box 0) (begin (newline) 7)))
+                    `(lambda () (begin (newline) 7))
+                    #f)
+         (test-comp `(lambda () (,e? (begin (newline) 7) (box 0)))
+                    `(lambda () (begin (newline) 7))
+                    #f)
+         (test-comp `(lambda (x) (if (,e? x '(0)) (pair? x) 0))
+                    `(lambda (x) (if (,e? x '(0)) #t 0)))
+         (test-comp `(lambda (x) (if (,e? x (list 0)) (pair? x) 0))
+                    `(lambda (x) (if (,e? x (list 0)) #t 0)))
+         (test-comp `(lambda (x y) (car y) (if (,e? x y) (pair? x) 0))
+                    `(lambda (x y) (car y) (if (,e? x y) #t 0))))])
   (test-equal? 'eq?)
   (test-equal? 'eqv?)
   (test-equal? 'equal?))
@@ -1616,23 +1641,6 @@
               (let ([y (random)])
                 (begin0 y (set! y 5)))))
 
-(test-comp '(lambda (x y) (car x) (unbox y) #f)
-           '(lambda (x y) (car x) (unbox y) (eq? x y)))
-(test-comp '(lambda (x) (car x) #f)
-           '(lambda (x) (car x) (eq? x (box 0))))
-(test-comp '(lambda (x) (car x) #f)
-           '(lambda (x) (car x) (eq? (begin (newline) x) (box 0)))
-           #f)
-(test-comp '(lambda (x) (car x) #f)
-           '(lambda (x) (car x) (eq? x (begin (newline) (box 0))))
-           #f)
-(test-comp '(lambda () (begin (newline) 7))
-           '(lambda () (eq? (box 0) (begin (newline) 7)))
-           #f)
-(test-comp '(lambda () (begin (newline) 7))
-           '(lambda () (eq? (begin (newline) 7) (box 0)))
-           #f)
-
 ; It's necessary to use the random from #%kernel because otherwise
 ; the function will keep an unnecessary reference for the module that
 ; defines the random visible from racket/base.
@@ -2068,12 +2076,6 @@
 (test-comp '(lambda (x) (if (null? x) 1 0) null)
            '(lambda (x) (if (null? x) 1 0) x)
            #f)
-(test-comp '(lambda (x) (if (eq? x '(0)) #t 0))
-           '(lambda (x) (if (eq? x '(0)) (pair? x) 0)))
-(test-comp '(lambda (x) (if (eq? x (list 0)) #t 0))
-           '(lambda (x) (if (eq? x (list 0)) (pair? x) 0)))
-(test-comp '(lambda (x y) (car y) (if (eq? x y) #t 0))
-           '(lambda (x y) (car y) (if (eq? x y) (pair? x) 0)))
 (test-comp '(lambda (x) (if x 1 (list #f)))
            '(lambda (x) (if x 1 (list x))))
 
diff --git a/racket/src/racket/src/optimize.c b/racket/src/racket/src/optimize.c
index 98d1a9e964..14c7485bba 100644
--- a/racket/src/racket/src/optimize.c
+++ b/racket/src/racket/src/optimize.c
@@ -4192,13 +4192,29 @@ static Scheme_Object *finish_optimize_application3(Scheme_App3_Rec *app, Optimiz
     }
   }
 
-  if ((SAME_OBJ(app->rator, scheme_equal_proc)
+  if (SAME_OBJ(app->rator, scheme_equal_proc)
        || SAME_OBJ(app->rator, scheme_eqv_proc)
-       || SAME_OBJ(app->rator, scheme_eq_proc))
-      && equivalent_exprs(app->rand1, app->rand2, NULL, NULL, 0)) {
-    info->preserves_marks = 1;
-    info->single_result = 1;
-    return make_discarding_sequence_3(app->rand1, app->rand2, scheme_true, info);
+       || SAME_OBJ(app->rator, scheme_eq_proc)) {
+    if (equivalent_exprs(app->rand1, app->rand2, NULL, NULL, 0)) {
+      info->preserves_marks = 1;
+      info->single_result = 1;
+      return make_discarding_sequence_3(app->rand1, app->rand2, scheme_true, info);
+    }
+    {
+      Scheme_Object *pred1, *pred2;
+      pred1 = expr_implies_predicate(app->rand1, info);
+      if (pred1) {
+        pred2 = expr_implies_predicate(app->rand2, info);
+        if (pred2) {
+          if (predicate_implies_not(pred1, pred2)
+              || predicate_implies_not(pred2, pred1)) {
+            info->preserves_marks = 1;
+            info->single_result = 1;
+            return make_discarding_sequence_3(app->rand1, app->rand2, scheme_false, info);
+          }
+        }
+      }
+    }
   }
 
   /* Optimize `equal?' or `eqv?' test on certain types
@@ -4219,21 +4235,6 @@ static Scheme_Object *finish_optimize_application3(Scheme_App3_Rec *app, Optimiz
     }
   }
 
-  if (SAME_OBJ(app->rator, scheme_eq_proc)) {
-    Scheme_Object *pred1, *pred2;
-    pred1 = expr_implies_predicate(app->rand1, info);
-    if (pred1) {
-      pred2 = expr_implies_predicate(app->rand2, info);
-      if (pred2) {
-        if (predicate_implies_not(pred1, pred2) || predicate_implies_not(pred2, pred1)) {
-          info->preserves_marks = 1;
-          info->single_result = 1;
-          return make_discarding_sequence_3(app->rand1, app->rand2, scheme_false, info);
-        }
-      }
-    }
-  }
-
   info->preserves_marks = !!(rator_flags & LAMBDA_PRESERVES_MARKS);
   info->single_result = !!(rator_flags & LAMBDA_SINGLE_RESULT);
   if (rator_flags & LAMBDA_RESULT_TENTATIVE) {
@@ -4988,7 +4989,9 @@ static void add_types_for_t_branch(Scheme_Object *t, Optimize_Info *info, int fu
   } else if (SAME_TYPE(SCHEME_TYPE(t), scheme_application3_type)) {
     Scheme_App3_Rec *app = (Scheme_App3_Rec *)t;
     Scheme_Object *pred1, *pred2;
-    if (SAME_OBJ(app->rator, scheme_eq_proc)) {
+    if (SAME_OBJ(app->rator, scheme_eq_proc)
+        || SAME_OBJ(app->rator, scheme_eqv_proc)
+        || SAME_OBJ(app->rator, scheme_equal_proc)) {
       if (SAME_TYPE(SCHEME_TYPE(app->rand1), scheme_ir_local_type)) {
         pred1 = expr_implies_predicate(app->rand1, info);
         if (!pred1) {