diff --git a/core/src/main/scala/org/apache/spark/rdd/PairRDDFunctions.scala b/core/src/main/scala/org/apache/spark/rdd/PairRDDFunctions.scala
index e0bc75e244acb..cb26ab6d19791 100644
--- a/core/src/main/scala/org/apache/spark/rdd/PairRDDFunctions.scala
+++ b/core/src/main/scala/org/apache/spark/rdd/PairRDDFunctions.scala
@@ -217,6 +217,9 @@ class PairRDDFunctions[K, V](self: RDD[(K, V)])
    * the RDD to guarantee sample size with a 99.99% confidence; when sampling with replacement, we
    * need two additional passes over the RDD to guarantee sample size with a 99.99% confidence.
    *
+   * Note that if the sampling rate for any stratum is < 1e-10, we will throw an exception to
+   * avoid not being able to ever create the sample as an artifact of the RNG's quality.
+   *
    * @param withReplacement whether to sample with or without replacement
    * @param fractionByKey function mapping key to sampling rate
    * @param seed seed for the random number generator
@@ -227,6 +230,10 @@ class PairRDDFunctions[K, V](self: RDD[(K, V)])
       fractionByKey: K => Double,
       seed: Long = Utils.random.nextLong,
       exact: Boolean = true): RDD[(K, V)]= {
+
+    require(fractionByKey.asInstanceOf[Map[K, Double]].forall({case(k, v) => v >= 1e-10}),
+      "Unable to support sampling rates < 1e-10.")
+
     if (withReplacement) {
       val counts = if (exact) Some(this.countByKey()) else None
       val samplingFunc =
diff --git a/core/src/main/scala/org/apache/spark/rdd/RDD.scala b/core/src/main/scala/org/apache/spark/rdd/RDD.scala
index 2b49241c579a3..d1000ae21e66a 100644
--- a/core/src/main/scala/org/apache/spark/rdd/RDD.scala
+++ b/core/src/main/scala/org/apache/spark/rdd/RDD.scala
@@ -350,11 +350,13 @@ abstract class RDD[T: ClassTag](
 
   /**
    * Return a sampled subset of this RDD.
+   *
+   * fraction < 1e-10 not supported.
    */
   def sample(withReplacement: Boolean, 
       fraction: Double, 
       seed: Long = Utils.random.nextLong): RDD[T] = {
-    require(fraction >= 0.0, "Invalid fraction value: " + fraction)
+    require(fraction >= 1e-10, "Invalid fraction value: " + fraction)
     if (withReplacement) {
       new PartitionwiseSampledRDD[T, T](this, new PoissonSampler[T](fraction), seed)
     } else {