diff --git a/cuburn/code/iter.py b/cuburn/code/iter.py
index 757c302..4a1edca 100644
--- a/cuburn/code/iter.py
+++ b/cuburn/code/iter.py
@@ -166,7 +166,7 @@ void iter(mwc_st *msts, iter_info *infos, uint64_t accbuf_ptr) {
 
     if (threadIdx.y == 1 && threadIdx.x == 0) {
         float ditherwidth = {{packer.get("0.33 * cp.spatial_filter_radius")}};
-        float u0 = mwc_next_01(rctx);
+        float u0 = mwc_next_01(rctx) + 0.02f;
         float r = ditherwidth * sqrt(-2.0f * log2f(u0) / M_LOG2E);
 
         float u1 = 2.0f * M_PI * mwc_next_01(rctx);