diff --git a/NEWS.md b/NEWS.md
index e0d62e2..911384f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,9 +1,13 @@
 # dqrng (unreleased)
 
 * Add R side support for selecting multiple streams for parallel usage.
-* Implement `long_jump()` for Xo(ro)shiro as alternative to `jump()` providing fewer streams with longer period.
+* Implement `long_jump()` for Xo(ro)shiro as alternative to `jump()`
+  providing fewer streams with longer period.
 * Handle R's RNG scope properly during initialisation.
-* New functions `dqsample` and `dqsample.int` using an unbiased sampling algorithm
+* New functions `dqsample` and `dqsample.int` using an unbiased sampling
+  algorithm.
+* Use `R_unif_index()` instead of `unif_rand()` to retrieve random data
+  from R's RNG in `generateSeedVectors()`.
 
 # dqrng 0.1.1
 
@@ -15,7 +19,7 @@
 ## Breaking changes
 
 * An integer vector instead of a single `int` is used for seeding (Aaron Lun in [#10](https://github.com/daqana/dqrng/pull/10))
-  * Single integer seeds lead to a different RNG state than before. 
+  * Single integer seeds lead to a different RNG state than before.
   * `dqrng::dqset_seed()` expects a `Rcpp::IntegerVector` instead of an `int`
 * Support for Mersenne-Twister has been removed, Xoroshiro128+ is now the default.
 
diff --git a/inst/include/R_randgen.h b/inst/include/R_randgen.h
index 63f60c2..039361d 100644
--- a/inst/include/R_randgen.h
+++ b/inst/include/R_randgen.h
@@ -5,14 +5,17 @@
 
 namespace dqrng {
 
-/* Create a uint32_t or int seed using R's PRNGs. 
- * The uint32_t seed is more convnient from use within C++,
+/* Create a uint32_t or int seed using R's PRNGs.
+ * The uint32_t seed is more convenient from use within C++,
  * the int seed is more convenient if it needs to be passed back to R.
+ * Since R's PRNG is used, calling one of these functions has to be shielded
+ * with calls to GetRNGState and PutRNGState, e.g. by using Rcpp::RNGScope.
+ * This is done automatically when using the Rcpp::export attribute.
  */
 
 inline uint32_t R_random_u32 () {
     constexpr double upper_limit=4294967296;
-    double val=R::unif_rand() * upper_limit;
+    double val = R_unif_index(upper_limit);
     if (val >= upper_limit) { val=0; } // Absolutely avoid overflow.
     return static_cast<uint32_t>(val);
 }
@@ -20,10 +23,10 @@ inline uint32_t R_random_u32 () {
 inline int R_random_int () {
     const uint32_t sampled=R_random_u32();
     constexpr uint32_t max_int=2147483647; // See .Machine$integer.max.
-    if (sampled <= max_int) { 
+    if (sampled <= max_int) {
         return static_cast<int>(sampled);
     }
-    
+
     // Effectively reverse of the int->uint32_t cast.
     constexpr uint32_t max_uint=-1;
     return -static_cast<int>(max_uint - sampled) - 1;