diff --git a/pymc/distributions/discrete.py b/pymc/distributions/discrete.py
index f5ba04c2acf..73c26b8fd08 100644
--- a/pymc/distributions/discrete.py
+++ b/pymc/distributions/discrete.py
@@ -738,14 +738,24 @@ def logp(value, theta, lam):
         -------
         TensorVariable
         """
-        log_prob = bound(np.log(theta) + logpow(theta + lam * value, value - 1)
-                         - (theta + lam * value) - factln(value),
-                         theta > 0,
-                         -1 <= lam, -theta/4 <= lam, lam <= 1,
-                         value >= 0)
+        theta_lam_value = theta + lam * value
+        log_prob = (
+            np.log(theta)
+            + logpow(theta_lam_value, value - 1) 
+            - theta_lam_value - factln(value)
+        )
+        
         # Probability is 0 when value > m, where m is the largest positive integer for which
         # theta + m * lam > 0 (when lam < 0).
-        return at.switch(theta + value * lam <= 0, -np.inf, log_prob)
+        log_prob = at.switch(theta_lam_value <= 0, -np.inf, log_prob)
+        
+        return bound(
+            log_prob,
+            value >= 0,
+            theta > 0,
+            abs(lam) <= 1, 
+            -theta/4 <= lam, 
+        )
 
 
 class NegativeBinomial(Discrete):