diff --git a/lightning/impl/penalty.py b/lightning/impl/penalty.py
index 6708e399..56614fdf 100644
--- a/lightning/impl/penalty.py
+++ b/lightning/impl/penalty.py
@@ -53,6 +53,9 @@ def regularization(self, coef):
 # See https://gist.github.com/mblondel/6f3b7aaad90606b98f71
 # for more algorithms.
 def project_simplex(v, z=1):
+    if np.sum(v) <= z:
+        return v
+
     n_features = v.shape[0]
     u = np.sort(v)[::-1]
     cssv = np.cumsum(u) - z
diff --git a/lightning/impl/tests/test_penalty.py b/lightning/impl/tests/test_penalty.py
index 418dc5fe..5fce5c8e 100644
--- a/lightning/impl/tests/test_penalty.py
+++ b/lightning/impl/tests/test_penalty.py
@@ -1,7 +1,45 @@
 import numpy as np
-from sklearn.utils.testing import assert_almost_equal
+from sklearn.utils.testing import assert_almost_equal, assert_array_almost_equal
 
-from lightning.impl.penalty import project_l1_ball
+from lightning.impl.penalty import project_l1_ball, project_simplex
+
+
+def project_simplex_bisection(v, z=1, tau=0.0001, max_iter=1000):
+    lower = 0
+    upper = np.max(v)
+    current = np.inf
+
+    for it in xrange(max_iter):
+        if np.abs(current) / z < tau and current < 0:
+            break
+
+        theta = (upper + lower) / 2.0
+        w = np.maximum(v - theta, 0)
+        current = np.sum(w) - z
+        if current <= 0:
+            upper = theta
+        else:
+            lower = theta
+    return w
+
+
+def test_proj_simplex():
+    rng = np.random.RandomState(0)
+
+    v = rng.rand(100)
+    w = project_simplex(v, z=10)
+    w2 = project_simplex_bisection(v, z=10, max_iter=100)
+    assert_array_almost_equal(w, w2, 3)
+
+    v = rng.rand(3)
+    w = project_simplex(v, z=1)
+    w2 = project_simplex_bisection(v, z=1, max_iter=100)
+    assert_array_almost_equal(w, w2, 3)
+
+    v = rng.rand(2)
+    w = project_simplex(v, z=1)
+    w2 = project_simplex_bisection(v, z=1, max_iter=100)
+    assert_array_almost_equal(w, w2, 3)
 
 
 def test_proj_l1_ball():