diff --git a/src/univariate/discrete/poisson.jl b/src/univariate/discrete/poisson.jl
index f6f3bb886..f91499f38 100644
--- a/src/univariate/discrete/poisson.jl
+++ b/src/univariate/discrete/poisson.jl
@@ -1,11 +1,11 @@
 immutable Poisson <: DiscreteUnivariateDistribution
     λ::Float64
 
-    Poisson(λ::Real) = (@check_args(Poisson, λ > zero(λ)); new(λ))
+    Poisson(λ::Real) = (@check_args(Poisson, λ >= zero(λ)); new(λ))
     Poisson() = new(1.0)
 end
 
-@distr_support Poisson 0 Inf
+@distr_support Poisson 0 (d.λ == 0.0 ? 0 : Inf)
 
 
 ### Parameters
@@ -34,7 +34,9 @@ kurtosis(d::Poisson) = 1.0 / d.λ
 
 function entropy(d::Poisson)
     λ = rate(d)
-    if λ < 50.0
+    if λ == 0.0
+        return 0.0
+    elseif λ < 50.0
         s = 0.0
         λk = 1.0
         for k = 1:100
diff --git a/test/discrete_test.json b/test/discrete_test.json
index bb5a65b21..9f1d9447e 100644
--- a/test/discrete_test.json
+++ b/test/discrete_test.json
@@ -1375,6 +1375,33 @@
       "var": 1.0
     }
   ], 
+  [
+    "Poisson(0.0)", 
+    {
+      "dtype": "Poisson", 
+        "entropy": 0.0,
+      "maximum": 0, 
+      "mean": 0.0, 
+      "median": 0.0, 
+      "minimum": 0, 
+      "params": {
+        "rate": 0.0
+      }, 
+      "points": [
+        {
+          "cdf": 1.0, 
+          "logpdf": 0.0, 
+          "x": 0
+        }
+      ], 
+      "q10": 0.0, 
+      "q25": 0.0, 
+      "q50": 0.0, 
+      "q75": 0.0, 
+      "q90": 0.0, 
+      "var": 0.0
+    }
+  ], 
   [
     "Poisson(0.5)", 
     {