diff --git a/collects/plot/plot2d/bounds.rkt b/collects/plot/plot2d/bounds.rkt
index 554d436920..5d440f3603 100644
--- a/collects/plot/plot2d/bounds.rkt
+++ b/collects/plot/plot2d/bounds.rkt
@@ -17,9 +17,9 @@
 ;; Attempts to comptute a fixpoint of, roughly, the bounds functions for the given renderers.
 ;; More precisely, starting with the given plot bounds, it attempts to compute a fixpoint of
 ;; apply-bounds*, overridden at every iteration by the plot bounds (if given).
-;; Because a fixpoint doesn't always exist, or only exists in the limit, it stops after max-iters.
+;; Because a fixpoint doesn't always exist, or may only exist in the limit, it stops after max-iters.
 (define (renderer2d-bounds-fixpoint renderers plot-x-min plot-x-max plot-y-min plot-y-max
-                                    [max-iters 4])
+                                    [max-iters 2])
   (let/ec break
     ;; Shortcut eval: if the plot bounds are all specified, the code below just returns them
     (when (and plot-x-min plot-x-max plot-y-min plot-y-max)
@@ -61,18 +61,14 @@
   (cond [(and x-min x-max)  (match-define (list xs ys) (f x-min x-max samples))
                             (define rys (filter regular? ys))
                             (cond [(empty? rys)  (values x-min x-max y-min y-max)]
-                                  [else  (values x-min x-max
-                                                 (if y-min y-min (apply min* rys))
-                                                 (if y-max y-max (apply max* rys)))])]
+                                  [else  (values x-min x-max (apply min* rys) (apply max* rys))])]
         [else  (values x-min x-max y-min y-max)]))
 
 (define ((inverse-bounds-fun f samples) x-min x-max y-min y-max)
   (cond [(and y-min y-max)  (match-define (list ys xs) (f y-min y-max samples))
                             (define rxs (filter regular? xs))
                             (cond [(empty? rxs)  (values x-min x-max y-min y-max)]
-                                  [else  (values (if x-min x-min (apply min* rxs))
-                                                 (if x-max x-max (apply max* rxs))
-                                                 y-min y-max)])]
+                                  [else  (values (apply min* rxs) (apply max* rxs) y-min y-max)])]
         [else  (values x-min x-max y-min y-max)]))
 
 (define ((function-interval-bounds-fun f1 f2 samples) x-min x-max y-min y-max)
@@ -81,9 +77,7 @@
          (match-define (list x2s y2s) (f2 x-min x-max samples))
          (define rys (filter regular? (append y1s y2s)))
          (cond [(empty? rys)  (values x-min x-max y-min y-max)]
-               [else  (values x-min x-max
-                              (if y-min y-min (apply min* rys))
-                              (if y-max y-max (apply max* rys)))])]
+               [else  (values x-min x-max (apply min* rys) (apply max* rys))])]
         [else  (values x-min x-max y-min y-max)]))
 
 (define ((inverse-interval-bounds-fun f1 f2 samples) x-min x-max y-min y-max)
@@ -92,7 +86,5 @@
          (match-define (list y2s x2s) (f2 y-min y-max samples))
          (define rxs (filter regular? (append x1s x2s)))
          (cond [(empty? rxs)  (values x-min x-max y-min y-max)]
-               [else  (values (if x-min x-min (apply min* rxs))
-                              (if x-max x-max (apply max* rxs))
-                              y-min y-max)])]
+               [else  (values (apply min* rxs) (apply max* rxs) y-min y-max)])]
         [else  (values x-min x-max y-min y-max)]))
diff --git a/collects/plot/plot3d/bounds.rkt b/collects/plot/plot3d/bounds.rkt
index 09a04b00f0..ed66b7b0af 100644
--- a/collects/plot/plot3d/bounds.rkt
+++ b/collects/plot/plot3d/bounds.rkt
@@ -15,9 +15,9 @@
 ;; Attempts to comptute a fixpoint of, roughly, the bounds functions for the given renderers.
 ;; More precisely, starting with the given plot bounds, it attempts to compute a fixpoint of
 ;; apply-bounds*, overridden at every iteration by the plot bounds (if given).
-;; Because a fixpoint doesn't always exist, or only exists in the limit, it stops after max-iters.
+;; Because a fixpoint doesn't always exist, or may only exist in the limit, it stops after max-iters.
 (define (renderer3d-bounds-fixpoint renderers plot-x-min plot-x-max plot-y-min plot-y-max
-                                    plot-z-min plot-z-max [max-iters 4])
+                                    plot-z-min plot-z-max [max-iters 2])
   (let/ec break
     ;; Shortcut eval: if the plot bounds are all specified, the code below just returns them
     (when (and plot-x-min plot-x-max plot-y-min plot-y-max plot-z-min plot-z-max)
@@ -65,7 +65,5 @@
          (match-define (list xs ys zss) (f x-min x-max samples y-min y-max samples))
          (define zs (filter regular? (2d-sample->list zss)))
          (cond [(empty? zs)  (values x-min x-max y-min y-max z-min z-max)]
-               [else  (values x-min x-max y-min y-max
-                              (if z-min z-min (apply min* zs))
-                              (if z-max z-max (apply max* zs)))])]
+               [else  (values x-min x-max y-min y-max (apply min* zs) (apply max* zs))])]
         [else  (values x-min x-max y-min y-max z-min z-max)]))
diff --git a/collects/plot/tests/plot2d-tests.rkt b/collects/plot/tests/plot2d-tests.rkt
index 9db7b8634a..c7165bd497 100644
--- a/collects/plot/tests/plot2d-tests.rkt
+++ b/collects/plot/tests/plot2d-tests.rkt
@@ -1,7 +1,6 @@
 #lang racket
 
-(require "../main.rkt"
-         "../utils.rkt")
+(require rackunit plot plot/utils)
 
 ;(plot-new-window? #t)
 
@@ -137,9 +136,10 @@
                       #:color "blue")
             (axes 1 0 #:y-ticks? #f)))
 
-#;; error: could not determine x bounds
-(plot (list (function sqr #f -1)
-            (function sqr 1 #f)))
+;; error: could not determine x bounds
+(check-exn exn:fail?
+           (λ () (plot (list (function sqr #f -1)
+                             (function sqr 1 #f)))))
 
 ; draws first function with x in [-2,-1]
 (plot (list (function sqr #f -1)
@@ -156,6 +156,10 @@
             (function sqr 1 #f))
       #:x-min -2 #:x-max 2)
 
+; draws both in full (particularly, without chopping off the top of the parabola), in [-2,2]
+(plot (list (function sqr)
+            (function sin -2 2)))
+
 (time
  (plot (list (discrete-histogram
               (build-list 10 (λ (n) (vector (string-ref "abcdefghij" n)