diff --git a/collects/rnrs/bytevectors-6.ss b/collects/rnrs/bytevectors-6.ss
index 9f9a6ccc70..dc26a0e069 100644
--- a/collects/rnrs/bytevectors-6.ss
+++ b/collects/rnrs/bytevectors-6.ss
@@ -186,6 +186,13 @@
                 bytevector-s64-native-set!)
   (make-integer-ops 8))
 
+(define (check-offset size k)
+  (unless (and (exact-nonnegative-integer? k)
+               (zero? (bitwise-and (sub1 size) k)))
+    (raise-type-error 'bytevector-operation 
+                      (format "exact nonnegative integer multiple of ~a" size)
+                      k)))
+
 (define (make-ieee-ops size)
   (values
    ;; -ref
@@ -194,6 +201,7 @@
      (floating-point-bytes->real bytes (eq? endianness 'big) k (+ k size)))
    ;; -native-ref
    (lambda (bytes k)
+     (check-offset size k)
      (floating-point-bytes->real bytes (system-big-endian?) k (+ k size)))
    ;; -set!
    (lambda (bytes k n endianness)
@@ -201,6 +209,7 @@
      (real->floating-point-bytes n size (eq? endianness 'big) bytes k))
    ;; -native-set!
    (lambda (bytes k n)
+     (check-offset size k)
      (real->floating-point-bytes n size (system-big-endian?) bytes k)
      (void))))
 
diff --git a/collects/tests/r6rs/bytevectors.sls b/collects/tests/r6rs/bytevectors.sls
index 19198af649..f2b00a75a9 100644
--- a/collects/tests/r6rs/bytevectors.sls
+++ b/collects/tests/r6rs/bytevectors.sls
@@ -136,23 +136,31 @@
       (test (bytevector-s64-ref b 8 (endianness little)) -144115188075855873)
       (test (bytevector-u64-ref b 8 (endianness big)) 18446744073709551613)
       (test (bytevector-s64-ref b 8 (endianness big)) -3))
-
+      
     (for-each
      (lambda (k)
        (for-each
         (lambda (n)
-          (let ([b (make-bytevector 12)])
-            (test/unspec (bytevector-ieee-single-native-set! b k n))
-            (test/approx (bytevector-ieee-single-native-ref b k) n))
+          (if (zero? (fxand k 3))
+              (let ([b (make-bytevector 12)])
+                (test/unspec (bytevector-ieee-single-native-set! b k n))
+                (test/approx (bytevector-ieee-single-native-ref b k) n))
+              (let ([b (make-bytevector 12)])
+                (test/exn (bytevector-ieee-single-native-set! b k n) &assertion)
+                (test/exn (bytevector-ieee-single-native-ref b k) &assertion)))
           (let ([b (make-bytevector 12)])
             (test/unspec (bytevector-ieee-single-set! b k n 'big))
             (test/approx (bytevector-ieee-single-ref b k 'big) n))
           (let ([b (make-bytevector 12)])
             (test/unspec (bytevector-ieee-single-set! b k n 'little))
             (test/approx (bytevector-ieee-single-ref b k 'little) n))
-          (let ([b (make-bytevector 12)])
-            (test/unspec (bytevector-ieee-double-native-set! b k n))
-            (test/approx (bytevector-ieee-double-native-ref b k) n))
+          (if (zero? (fxand k 7))
+              (let ([b (make-bytevector 12)])
+                (test/unspec (bytevector-ieee-double-native-set! b k n))
+                (test/approx (bytevector-ieee-double-native-ref b k) n))
+              (let ([b (make-bytevector 12)])
+                (test/exn (bytevector-ieee-double-native-set! b k n) &assertion)
+                (test/exn (bytevector-ieee-double-native-ref b k) &assertion)))
           (let ([b (make-bytevector 12)])
             (test/unspec (bytevector-ieee-double-set! b k n 'big))
             (test/approx (bytevector-ieee-double-ref b k 'big) n))