diff --git a/collects/tests/mzscheme/number.ss b/collects/tests/mzscheme/number.ss
index 8282c66f9c..8f87c76dcc 100644
--- a/collects/tests/mzscheme/number.ss
+++ b/collects/tests/mzscheme/number.ss
@@ -1002,9 +1002,13 @@
 (test #x-155553333 bitwise-xor #x-2aaaa5555 (bitwise-xor #x-2aaaa5555 #x-155553333))
 (test #x-15555333 bitwise-xor #x-2aaaa5555 (bitwise-xor #x-2aaaa5555 #x-15555333))
 
-(arity-test bitwise-ior 1 -1)
-(arity-test bitwise-and 1 -1)
-(arity-test bitwise-xor 1 -1)
+(test -1 bitwise-and)
+(test 0 bitwise-ior)
+(test 0 bitwise-xor)
+
+(arity-test bitwise-ior 0 -1)
+(arity-test bitwise-and 0 -1)
+(arity-test bitwise-xor 0 -1)
 (arity-test bitwise-not 1 1)
 
 (define error-test-bitwise-procs
diff --git a/collects/tests/mzscheme/optimize.ss b/collects/tests/mzscheme/optimize.ss
index d07c001c60..16c6e370dd 100644
--- a/collects/tests/mzscheme/optimize.ss
+++ b/collects/tests/mzscheme/optimize.ss
@@ -57,6 +57,7 @@
 		     (test (if v 'yes 'no) name ((eval `(lambda (x) (if (,op ,arg1 x) 'yes 'no))) arg2)))))]
 	 [bin-exact (lambda (v op arg1 arg2)
 		      (check-error-message op (eval `(lambda (x) (,op x ,arg2))))
+		      (check-error-message op (eval `(lambda (x) (,op ,arg1 x))))
 		      (bin0 v op arg1 arg2))]
 	 [bin (lambda (v op arg1 arg2)
 		(bin-exact v op arg1 arg2)
@@ -193,6 +194,19 @@
     (un-exact (- (expt 2 30)) 'bitwise-not (sub1 (expt 2 30)))
     (un-exact (- -1 (expt 2 32)) 'bitwise-not (expt 2 32))
 
+    (bin-exact 'a 'vector-ref #(a b c) 0)
+    (bin-exact 'b 'vector-ref #(a b c) 1)
+    (bin-exact 'c 'vector-ref #(a b c) 2)
+
+    (bin-exact #\a 'string-ref "abc\u2001" 0)
+    (bin-exact #\b 'string-ref "abc\u2001" 1)
+    (bin-exact #\c 'string-ref "abc\u2001" 2)
+    (bin-exact #\u2001 'string-ref "abc\u2001" 3)
+
+    (bin-exact 65 'bytes-ref #"Abc\xF7" 0)
+    (bin-exact 99 'bytes-ref #"Abc\xF7" 2)
+    (bin-exact #xF7 'bytes-ref #"Abc\xF7" 3)
+
     ))
 
 ;; For some comparison, ignore the stack-depth
diff --git a/collects/tests/mzscheme/stx.ss b/collects/tests/mzscheme/stx.ss
index 198a5a6738..106f0ac8c7 100644
--- a/collects/tests/mzscheme/stx.ss
+++ b/collects/tests/mzscheme/stx.ss
@@ -1007,5 +1007,35 @@
   (go-once (lambda (e) (eval (expand e)))))
 
 ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; layers of lexical binding
+
+(test '(1 2) 'macro-nested-lexical
+      (let ()
+	(define-syntax (m stx)
+	  (with-syntax ([x1 (let ([x 0]) #'x)]
+			[x2 (let ([x 0]) #'x)])
+	    #'(begin
+		(define x1 1)	
+		(define x2 2)
+		(list x1 x2))))
+	(m)))
+
+(module @!$m mzscheme
+  (define-syntax (d stx)
+    (syntax-case stx ()
+      [(_ id)
+       (with-syntax ([x1 (let ([x 0]) #'x)]
+		     [x2 (let ([x 0]) #'x)])
+	 #'(begin
+	     (define x1 10)
+	     (define x2 20)
+	     (define id (list x1 x2
+			      (list? (identifier-binding (quote-syntax x1)))))))]))
+  (d @!$get)
+  (provide @!$get))
+(require @!$m)
+(test '(10 20 #t) '@!$get @!$get)
+
+
 
 (report-errs)