diff --git a/Python/random.c b/Python/random.c
index ea09e84..1d57b1b 100644
--- a/Python/random.c
+++ b/Python/random.c
@@ -6,7 +6,9 @@
 #  ifdef HAVE_SYS_STAT_H
 #    include <sys/stat.h>
 #  endif
-#  ifdef HAVE_GETRANDOM_SYSCALL
+#  ifdef HAVE_GETRANDOM
+#    include <sys/random.h>
+#  elif defined(HAVE_GETRANDOM_SYSCALL)
 #    include <sys/syscall.h>
 #  endif
 #endif
@@ -70,7 +72,9 @@
     return 0;
 }
 
-#elif HAVE_GETENTROPY
+#elif defined(HAVE_GETENTROPY) && !defined(sun)
+#define PY_GETENTROPY 1
+
 /* Fill buffer with size pseudo-random bytes generated by getentropy().
    Return 0 on success, or raise an exception and return -1 on error.
 
@@ -105,16 +109,19 @@
     return 0;
 }
 
-#else   /* !HAVE_GETENTROPY */
+#else
 
-#ifdef HAVE_GETRANDOM_SYSCALL
+#if defined(HAVE_GETRANDOM) || defined(HAVE_GETRANDOM_SYSCALL)
+#define PY_GETRANDOM 1
+
 static int
 py_getrandom(void *buffer, Py_ssize_t size, int raise)
 {
-    /* is getrandom() supported by the running kernel?
-     * need Linux kernel 3.17 or later */
+    /* Is getrandom() supported by the running kernel?
+     * Need Linux kernel 3.17 or newer, or Solaris 11.3 or newer */
     static int getrandom_works = 1;
-    /* Use /dev/urandom, block if the kernel has no entropy */
+    /* Use non-blocking /dev/urandom device. On Linux at boot, the getrandom()
+     * syscall blocks until /dev/urandom is initialized with enough entropy. */
     const int flags = 0;
     int n;
 
@@ -124,7 +131,18 @@
     while (0 < size) {
         errno = 0;
 
-        /* Use syscall() because the libc doesn't expose getrandom() yet, see:
+#ifdef HAVE_GETRANDOM
+        if (raise) {
+            Py_BEGIN_ALLOW_THREADS
+            n = getrandom(buffer, size, flags);
+            Py_END_ALLOW_THREADS
+        }
+        else {
+            n = getrandom(buffer, size, flags);
+        }
+#else
+        /* On Linux, use the syscall() function because the GNU libc doesn't
+         * expose the Linux getrandom() syscall yet. See:
          * https://sourceware.org/bugzilla/show_bug.cgi?id=17252 */
         if (raise) {
             Py_BEGIN_ALLOW_THREADS
@@ -134,6 +152,7 @@
         else {
             n = syscall(SYS_getrandom, buffer, size, flags);
         }
+#endif
 
         if (n < 0) {
             if (errno == ENOSYS) {
@@ -182,7 +201,7 @@
 
     assert (0 < size);
 
-#ifdef HAVE_GETRANDOM_SYSCALL
+#ifdef PY_GETRANDOM
     if (py_getrandom(buffer, size, 0) == 1)
         return;
     /* getrandom() is not supported by the running kernel, fall back
@@ -218,14 +237,14 @@
     int fd;
     Py_ssize_t n;
     struct _Py_stat_struct st;
-#ifdef HAVE_GETRANDOM_SYSCALL
+#ifdef PY_GETRANDOM
     int res;
 #endif
 
     if (size <= 0)
         return 0;
 
-#ifdef HAVE_GETRANDOM_SYSCALL
+#ifdef PY_GETRANDOM
     res = py_getrandom(buffer, size, 1);
     if (res < 0)
         return -1;
@@ -304,7 +323,7 @@
     }
 }
 
-#endif /* HAVE_GETENTROPY */
+#endif
 
 /* Fill buffer with pseudo-random bytes generated by a linear congruent
    generator (LCG):
@@ -345,7 +364,7 @@
 
 #ifdef MS_WINDOWS
     return win32_urandom((unsigned char *)buffer, size, 1);
-#elif HAVE_GETENTROPY
+#elif defined(PY_GETENTROPY)
     return py_getentropy(buffer, size, 0);
 #else
     return dev_urandom_python((char*)buffer, size);
@@ -392,7 +411,7 @@
     else {
 #ifdef MS_WINDOWS
         (void)win32_urandom(secret, secret_size, 0);
-#elif HAVE_GETENTROPY
+#elif defined(PY_GETENTROPY)
         (void)py_getentropy(secret, secret_size, 1);
 #else
         dev_urandom_noraise(secret, secret_size);
@@ -408,7 +427,7 @@
         CryptReleaseContext(hCryptProv, 0);
         hCryptProv = 0;
     }
-#elif HAVE_GETENTROPY
+#elif defined(PY_GETENTROPY)
     /* nothing to clean */
 #else
     dev_urandom_close();