diff --git a/hexrd/powder/wppf/WPPF.py b/hexrd/powder/wppf/WPPF.py
index a468f307..8f6ed33e 100644
--- a/hexrd/powder/wppf/WPPF.py
+++ b/hexrd/powder/wppf/WPPF.py
@@ -2023,7 +2023,7 @@ def computespectrum_2D(self):
             simulated_2d = np.empty([nspec, x.shape[0]])
             azimuth_texture_factor = {}
             for iph, p in enumerate(self.phases):
-                if p in self.texture_model:
+                if self.texture_model.get(p) is not None:
                     self.texture_model[p].calc_pf_rings(
                         self.params,
                         eta_min=self.eta_min,
@@ -2112,15 +2112,20 @@ def Refine(self):
             print("Nothing to refine...")
 
     def RefineTexture(self):
+        final_result = None
         for name, model in self.texture_model.items():
             if model is None:
                 continue
 
             print(f'Refining texture parameters for "{name}"')
             results = model.calculate_harmonic_coefficients(self.params)
+            if results is None:
+                print(f'No "{name}" parameters marked as "vary". Skipping...')
+
+            final_result = results if results is not None else final_result
 
         # Set the results to the final one
-        self.res = results
+        self.res = final_result
 
         self.computespectrum()
         self.niter += 1
@@ -2156,7 +2161,7 @@ def any_texture_params_varied(self):
     @property
     def texture_models_have_pfdata(self):
         for model in self.texture_model.values():
-            if not model.pfdata:
+            if model is not None and not model.pfdata:
                 return False
 
         return True
@@ -2419,6 +2424,9 @@ def compute_texture_data(
             if model is None:
                 continue
 
+            # Sanitize the name
+            mat_key = mat_key.replace('-', '_')
+
             pfdata = {}
             for ii, nnz in enumerate(results[3]):
                 eta = self.eta_min + (nnz + 1) * np.radians(azimuthal_interval)
diff --git a/hexrd/powder/wppf/texture.py b/hexrd/powder/wppf/texture.py
index 3cd9112c..af3f7c26 100644
--- a/hexrd/powder/wppf/texture.py
+++ b/hexrd/powder/wppf/texture.py
@@ -1554,6 +1554,10 @@ def calculate_harmonic_coefficients(self, params, hkls=None):
         for name in self.parameter_names:
             harmonic_params[name] = copy.deepcopy(params[name])
 
+        if not any(param.vary for param in harmonic_params.values()):
+            # No parameters are marked as vary. Return early.
+            return None
+
         self.sph_c = {}
         self.sph_s = {}