diff --git a/racket/src/ChezScheme/c/externs.h b/racket/src/ChezScheme/c/externs.h
index 526d5c0eca..54a8979988 100644
--- a/racket/src/ChezScheme/c/externs.h
+++ b/racket/src/ChezScheme/c/externs.h
@@ -313,6 +313,7 @@ extern ptr S_gcd PROTO((ptr x, ptr y));
 extern ptr S_ash PROTO((ptr x, ptr n));
 extern ptr S_big_positive_bit_field PROTO((ptr x, ptr fxstart, ptr fxend));
 extern ptr S_integer_length PROTO((ptr x));
+extern ptr S_big_trailing_zero_bits PROTO((ptr x));
 extern ptr S_big_first_bit_set PROTO((ptr x));
 extern double S_random_double PROTO((U32 m1, U32 m2,
                U32 m3, U32 m4, double scale));
diff --git a/racket/src/ChezScheme/c/number.c b/racket/src/ChezScheme/c/number.c
index dd6c1274df..2585c18440 100644
--- a/racket/src/ChezScheme/c/number.c
+++ b/racket/src/ChezScheme/c/number.c
@@ -1481,6 +1481,23 @@ ptr S_big_positive_bit_field(ptr x, ptr fxstart, ptr fxend) {
   return copy_normalize(tc, &BIGIT(W(tc), 0), wl, 0);
 }
 
+/* returns a lower bound on the number of trailing 0 bits in the
+   binary representation: */
+ptr S_big_trailing_zero_bits(ptr x) {
+  bigit *xp = &BIGIT(x, 0);
+  iptr xl = BIGLEN(x), i;
+
+  for (i = xl; i-- > 0; ) {
+    if (xp[i] != 0)
+      break;
+  }
+
+  i = (xl - 1) - i;
+  i *= bigit_bits;
+
+  return FIX(i);
+}
+
 /* logical operations simulate two's complement operations using the
    following general strategy:
 
diff --git a/racket/src/ChezScheme/c/prim5.c b/racket/src/ChezScheme/c/prim5.c
index 01e4b7be60..6f618cf80e 100644
--- a/racket/src/ChezScheme/c/prim5.c
+++ b/racket/src/ChezScheme/c/prim5.c
@@ -1765,6 +1765,7 @@ void S_prim5_init() {
     Sforeign_symbol("(cs)s_big_positive_bit_field", (void *)S_big_positive_bit_field);
     Sforeign_symbol("(cs)s_big_eq", (void *)S_big_eq);
     Sforeign_symbol("(cs)s_big_lt", (void *)S_big_lt);
+    Sforeign_symbol("(cs)s_big_trailing_zero_bits", (void *)S_big_trailing_zero_bits);
     Sforeign_symbol("(cs)s_bigoddp", (void *)s_bigoddp);
     Sforeign_symbol("(cs)s_div", (void *)S_div);
     Sforeign_symbol("(cs)s_float", (void *)s_float);
diff --git a/racket/src/ChezScheme/s/5_3.ss b/racket/src/ChezScheme/s/5_3.ss
index c253c7d8f0..ae4752a035 100644
--- a/racket/src/ChezScheme/s/5_3.ss
+++ b/racket/src/ChezScheme/s/5_3.ss
@@ -2197,6 +2197,7 @@
           [else (nonnumber-error who x)])])))
 
 (set! $*
+  (let ([$bignum-trailing-zero-bits (foreign-procedure "(cs)s_big_trailing_zero_bits" (ptr) ptr)])
    (lambda (who x y)
     (cond
       [(and (fixnum? y) ($fxu< (#3%fx+ y 1) 3))
@@ -2217,7 +2218,7 @@
                               [(fx= x 1) (unless (number? y) (nonnumber-error who y)) y]
                               [else ($negate who y)])]
                             [else (integer* x y)])
-                            (let ()
+                           (let ()
                               ;; _Modern Computer Arithmetic_, Brent and Zimmermann
                               (define (karatsuba x y)
                                 (define xl (if (bignum? x) ($bignum-length x) 0))
@@ -2247,7 +2248,17 @@
                                                    [else
                                                     (- c1 (karatsuba (- x-lo x-hi) (- y-lo y-hi)))])])])
                                     (+ c0 (integer-ash (+ c0 c1-c2) k) (integer-ash c1 (fx* 2 k))))]))
-                              (karatsuba x y)))]
+                              ;; Multiplying numbers with trailing 0s is common, so
+                              ;; check for that case:
+                              (let ([xz ($bignum-trailing-zero-bits x)]
+                                    [yz (if (bignum? y) ($bignum-trailing-zero-bits y) 0)])
+                                (let ([z (fx+ xz yz)])
+                                  (if (fx= z 0)
+                                      (karatsuba x y)
+                                      (bitwise-arithmetic-shift-left
+                                       (karatsuba (bitwise-arithmetic-shift-right x xz)
+                                                  (bitwise-arithmetic-shift-right y yz))
+                                       z))))))]
              [(ratnum?) (/ (* x ($ratio-numerator y)) ($ratio-denominator y))]
              [($exactnum? $inexactnum?)
               (make-rectangular (* x (real-part y)) (* x (imag-part y)))]
@@ -2281,7 +2292,7 @@
                     [c (real-part y)] [d (imag-part y)])
                 (make-rectangular (- (* a c) (* b d)) (+ (* a d) (* b c))))]
              [else (nonnumber-error who y)])]
-          [else (nonnumber-error who x)])])))
+          [else (nonnumber-error who x)])]))))
 
 (set! $-
   (lambda (who x y)