diff --git a/GPy/core/parameterization/priors.py b/GPy/core/parameterization/priors.py
index 71b9833e..eb83f83d 100644
--- a/GPy/core/parameterization/priors.py
+++ b/GPy/core/parameterization/priors.py
@@ -5,7 +5,7 @@
 import numpy as np
 from scipy.special import gammaln, digamma
 from ...util.linalg import pdinv
-from paramz.domains import _REAL, _POSITIVE
+from paramz.domains import _REAL, _POSITIVE, _NEGATIVE
 import warnings
 import weakref
 
@@ -92,7 +92,6 @@ class Gaussian(Prior):
 #         self.constant = -0.5 * np.log(2 * np.pi * self.sigma2)
 
 class Uniform(Prior):
-    domain = _REAL
     _instances = []
 
     def __new__(cls, lower=0, upper=1):  # Singleton:
@@ -108,6 +107,13 @@ class Uniform(Prior):
     def __init__(self, lower, upper):
         self.lower = float(lower)
         self.upper = float(upper)
+        assert self.lower < self.upper, "Lower needs to be strictly smaller than upper."
+        if self.lower >= 0:
+            self.domain = _POSITIVE
+        elif self.upper <= 0:
+            self.domain = _NEGATIVE
+        else:
+            self.domain = _REAL
 
     def __str__(self):
         return "[{:.2g}, {:.2g}]".format(self.lower, self.upper)