diff --git a/python/triton/code_gen.py b/python/triton/code_gen.py
index aedb2051f..699487232 100644
--- a/python/triton/code_gen.py
+++ b/python/triton/code_gen.py
@@ -588,7 +588,8 @@ class Kernel:
         torch.cuda.set_device(device_idx)
         # attributes
         args = [arg.data_ptr() if i in tensor_idxs else arg for i, arg in enumerate(wargs)]
-        attributes = {i: Kernel.pow2_divisor(a) for i, a in enumerate(args) if isinstance(a, int)}
+        attributes = {i: Kernel.pow2_divisor(a) for i, a in enumerate(args) \
+                      if isinstance(a, int) and i not in self.fn.do_not_specialize}
         # transforms ints whose value is one into constants for just-in-time compilation
         constants = {i: arg for i, arg in enumerate(wargs) if isinstance(arg, int) and arg == 1}
         # compute hash for caching this kernel
@@ -740,13 +741,15 @@ class JITFunction:
     def _set_cache_key(self):
         self.cache_key = (hashlib.md5(self.src.encode("utf-8")).hexdigest(), self.version)
 
-    def __init__(self, fn, version=None):
+    def __init__(self, fn, version=None, do_not_specialize=None):
         # information of wrapped function
         self.fn = fn
         self.module = fn.__module__
         self.arg_names = inspect.getfullargspec(fn).args
         self.version = version
         self.src = textwrap.dedent(inspect.getsource(fn))
+        self.do_not_specialize = [] if do_not_specialize is None else\
+                                 [self.arg_names.index(arg) for arg in do_not_specialize]
         # cache for callable driver objects (e.g. CUkernel)
         self.drv_cache = dict()
         # cache for binaries (on-disk)