diff --git a/VEX/priv/guest_amd64_toIR.c b/VEX/priv/guest_amd64_toIR.c
index 47a99ea52..34ebcbdf9 100644
--- a/VEX/priv/guest_amd64_toIR.c
+++ b/VEX/priv/guest_amd64_toIR.c
@@ -22079,12 +22079,8 @@ Long dis_ESC_0F (
       if (fAddr == &amd64g_dirtyhelper_CPUID_avx2
           || fAddr == &amd64g_dirtyhelper_CPUID_avx_and_cx16) {
          Bool hasF16C   = (archinfo->hwcaps & VEX_HWCAPS_AMD64_F16C) != 0;
-         /* A deterministic RNG still serves RDRAND/RDSEED but hides them. */
-         Bool advertiseRng = vex_random32 == NULL;
-         Bool hasRDRAND = advertiseRng
-                          && (archinfo->hwcaps & VEX_HWCAPS_AMD64_RDRAND) != 0;
-         Bool hasRDSEED = advertiseRng
-                          && (archinfo->hwcaps & VEX_HWCAPS_AMD64_RDSEED) != 0;
+         Bool hasRDRAND = (archinfo->hwcaps & VEX_HWCAPS_AMD64_RDRAND) != 0;
+         Bool hasRDSEED = (archinfo->hwcaps & VEX_HWCAPS_AMD64_RDSEED) != 0;
          args = mkIRExprVec_4(IRExpr_GSPTR(),
                               mkIRExpr_HWord(hasF16C ? 1 : 0),
                               mkIRExpr_HWord(hasRDRAND ? 1 : 0),
diff --git a/VEX/pub/libvex.h b/VEX/pub/libvex.h
index 1149038d0..564fe941d 100644
--- a/VEX/pub/libvex.h
+++ b/VEX/pub/libvex.h
@@ -689,8 +689,7 @@ extern void LibVEX_Init (
 );
 
 /* Install before guest execution. NULL preserves host RDRAND/RDSEED.
-   Otherwise CPUID hides them, and they return bits from this callback,
-   which runs on the executing guest thread. */
+   The callback runs on the executing guest thread and returns 32 random bits. */
 extern void LibVEX_SetRandom32 ( UInt (*random32)(void) );
 
 
diff --git a/docs/xml/manual-core.xml b/docs/xml/manual-core.xml
index e7b97474b..d82bea4b8 100644
--- a/docs/xml/manual-core.xml
+++ b/docs/xml/manual-core.xml
@@ -810,11 +810,10 @@ in most cases.  We group the available options by rough categories.</para>
         <computeroutput>/dev/random</computeroutput> and
         <computeroutput>/dev/urandom</computeroutput> (resolved
         through <computeroutput>/proc/self/fd</computeroutput>, so
-        symlinks count).  On amd64, CPUID does not report
-        <computeroutput>RDRAND</computeroutput> and
-        <computeroutput>RDSEED</computeroutput>.  On hosts that support them,
-        programs that execute them anyway draw from the calling thread's PRNG
-        stream, which always reports success.  On arm64,
+        symlinks count).  On amd64, <computeroutput>RDRAND</computeroutput>
+        and <computeroutput>RDSEED</computeroutput> draw from the calling
+        thread's PRNG stream and always report success.  CPUID still
+        reports them only when the host supports them.  On arm64,
         <computeroutput>RNDR</computeroutput> and
         <computeroutput>RNDRRS</computeroutput> draw from the same stream and
         always report success, also on hosts without FEAT_RNG.
diff --git a/none/tests/amd64/deterministic_rng.stdout.exp b/none/tests/amd64/deterministic_rng.stdout.exp
index a462030cb..cb97b860b 100644
--- a/none/tests/amd64/deterministic_rng.stdout.exp
+++ b/none/tests/amd64/deterministic_rng.stdout.exp
@@ -1,5 +1,5 @@
-cpuid rdrand: 0
-cpuid rdseed: 0
+cpuid rdrand: 1
+cpuid rdseed: 1
 rdrand16: 555555555555d78e
 rdrand16: 555555555555b519
 rdrand32: 00000000131a7a6b