diff --git a/python-backend/promptengine/template.py b/python-backend/promptengine/template.py
index 2d95b6b..41218d0 100644
--- a/python-backend/promptengine/template.py
+++ b/python-backend/promptengine/template.py
@@ -37,6 +37,12 @@ class PromptTemplate:
     def __repr__(self) -> str:
         return self.__str__()
     
+    def has_var(self, varname) -> bool:
+        """ Returns True if the template has a variable with the given name.
+        """
+        subbed_str = Template(self.template).safe_substitute({varname: '_'})
+        return subbed_str != self.template  # if the strings differ, a replacement occurred 
+
     def is_concrete(self) -> bool:
         """ Returns True if no template variables are left in template string.
         """
@@ -93,9 +99,18 @@ class PromptPermutationGenerator:
     def _gen_perm(self, template, params_to_fill, paramDict):
         if len(params_to_fill) == 0: return []
 
-        # Peel off first element
-        param = params_to_fill[0]
-        params_left = params_to_fill[1:]
+        # Extract the first param that occurs in the current template
+        param = None
+        params_left = params_to_fill
+        for p in params_to_fill:
+            if template.has_var(p):
+                param = p
+                params_left = [_p for _p in params_to_fill if _p != p]
+                break
+        
+        if param is None:
+            print("Did not find any more params left to fill in current template. Returning empty list...")
+            return []
 
         # Generate new prompts by filling in its value(s) into the PromptTemplate
         val = paramDict[param]
@@ -112,7 +127,7 @@ class PromptPermutationGenerator:
         else:
             res = []
             for p in new_prompt_temps:
-                res.extend(self._gen_perm(p, params_to_fill[1:], paramDict))
+                res.extend(self._gen_perm(p, params_left, paramDict))
             return res
 
     def __call__(self, paramDict: Dict[str, Union[str, List[str]]]):
@@ -121,4 +136,26 @@ class PromptPermutationGenerator:
             return
 
         for p in self._gen_perm(self.template, list(paramDict.keys()), paramDict):
-            yield p
\ No newline at end of file
+            yield p
+
+
+# Test cases
+if __name__ == '__main__':
+    # Single template
+    gen = PromptPermutationGenerator('What is the ${timeframe} when ${person} was born?')
+    res = [r for r in gen({'timeframe': ['year', 'decade', 'century'], 'person': ['Howard Hughes', 'Toni Morrison', 'Otis Redding']})]
+    for r in res:
+        print(r)
+    assert len(res) == 9
+
+    # Nested templates
+    gen = PromptPermutationGenerator('${prefix}... ${suffix}')
+    res = [r for r in gen({
+        'prefix': ['Who invented ${tool}?', 'When was ${tool} invented?', 'What can you do with ${tool}?'],
+        'suffix': ['Phrase your answer in the form of a ${response_type}', 'Respond with a ${response_type}'],
+        'tool': ['the flashlight', 'CRISPR', 'rubber'],
+        'response_type': ['question', 'poem', 'nightmare']
+    })]
+    for r in res:
+        print(r)
+    assert len(res) == (3*3)*(2*3)
\ No newline at end of file