diff --git a/bootstrap.conf b/bootstrap.conf
index 126e1e80a..43924c5b1 100644
--- a/bootstrap.conf
+++ b/bootstrap.conf
@@ -64,7 +64,6 @@ gnulib_modules="
   config-h
   configmake
   copy-file-range
-  count-leading-zeros
   crypto/md5
   crypto/sha1
   crypto/sha256
@@ -247,6 +246,7 @@ gnulib_modules="
   stat-size
   stat-time
   stdbool
+  stdc_leading_zeros
   stdckdint
   stdlib-safer
   stpcpy
diff --git a/gl/lib/randperm.c b/gl/lib/randperm.c
index 9903966e4..50328cd9a 100644
--- a/gl/lib/randperm.c
+++ b/gl/lib/randperm.c
@@ -22,28 +22,14 @@
 #include "randperm.h"
 
 #include <limits.h>
+#include <stdbit.h>
 #include <stdint.h>
 #include <stdlib.h>
 
 #include "attribute.h"
-#include "count-leading-zeros.h"
 #include "hash.h"
 #include "xalloc.h"
 
-/* Return the floor of the log base 2 of N.  If N is zero, return -1.  */
-
-ATTRIBUTE_CONST static int
-floor_lg (size_t n)
-{
-  static_assert (SIZE_WIDTH <= ULLONG_WIDTH);
-  return (n == 0 ? -1
-          : SIZE_WIDTH <= UINT_WIDTH
-          ? UINT_WIDTH - 1 - count_leading_zeros (n)
-          : SIZE_WIDTH <= ULONG_WIDTH
-          ? ULONG_WIDTH - 1 - count_leading_zeros_l (n)
-          : ULLONG_WIDTH - 1 - count_leading_zeros_ll (n));
-}
-
 /* Return an upper bound on the number of random bytes needed to
    generate the first H elements of a random permutation of N
    elements.  H must not exceed N.  */
@@ -53,7 +39,7 @@ randperm_bound (size_t h, size_t n)
 {
   /* Upper bound on number of bits needed to generate the first number
      of the permutation.  */
-  uintmax_t lg_n = floor_lg (n) + 1;
+  uintmax_t lg_n = stdc_bit_width (n) + 1;
 
   /* Upper bound on number of bits needed to generated the first H elements.  */
   uintmax_t ar = lg_n * h;
diff --git a/gl/modules/randperm b/gl/modules/randperm
index 5bb5faefc..ae54bf7ab 100644
--- a/gl/modules/randperm
+++ b/gl/modules/randperm
@@ -7,8 +7,8 @@ lib/randperm.h
 
 Depends-on:
 assert-h
-count-leading-zeros
 randint
+stdc_bit_width
 stdint
 xalloc
 hash
diff --git a/src/ioblksize.h b/src/ioblksize.h
index dcf94fc60..d6aabebeb 100644
--- a/src/ioblksize.h
+++ b/src/ioblksize.h
@@ -17,7 +17,7 @@
 /* Include this file _after_ system headers if possible.  */
 
 /* sys/stat.h and minmax.h will already have been included by system.h. */
-#include "count-leading-zeros.h"
+#include <stdbit.h>
 #include "stat-size.h"
 
 
@@ -94,7 +94,7 @@ io_blksize (struct stat const *st)
      power of two when the reported blocksize is not a power of two.  */
   if (S_ISREG (st->st_mode) && blocksize & (blocksize - 1))
     {
-      int leading_zeros = count_leading_zeros_ll (blocksize);
+      int leading_zeros = stdc_leading_zeros_ull (blocksize);
       if (IDX_MAX < ULLONG_MAX || leading_zeros)
         {
           unsigned long long power = 1ull << (ULLONG_WIDTH - leading_zeros);