diff --git a/CHANGELOG-unreleased.md b/CHANGELOG-unreleased.md
index d15e5e781..8e7b884e3 100644
--- a/CHANGELOG-unreleased.md
+++ b/CHANGELOG-unreleased.md
@@ -11,6 +11,8 @@ the released changes.
 ### Changed
 ### Added
 - When TCB->TDB conversion info is missing, will print parameter name
+- `add_param` returns the name of the parameter (useful for numbered parameters)
 ### Fixed
 - When EQUAD is created from TNEQ, has proper TCB->TDB conversion info
+- TOA selection masks will work when only TOA is the first one
 ### Removed
diff --git a/src/pint/models/noise_model.py b/src/pint/models/noise_model.py
index b1af8e10f..299787fe5 100644
--- a/src/pint/models/noise_model.py
+++ b/src/pint/models/noise_model.py
@@ -164,14 +164,14 @@ def scale_toa_sigma(self, toas, warn=True):
             if equad.quantity is None:
                 continue
             mask = equad.select_toa_mask(toas)
-            if np.any(mask):
+            if len(mask) > 0:
                 sigma_scaled[mask] = np.hypot(sigma_scaled[mask], equad.quantity)
             elif warn:
                 warnings.warn(f"EQUAD {equad} has no TOAs")
         for efac_name in self.EFACs:
             efac = getattr(self, efac_name)
             mask = efac.select_toa_mask(toas)
-            if np.any(mask):
+            if len(mask) > 0:
                 sigma_scaled[mask] *= efac.quantity
             elif warn:
                 warnings.warn(f"EFAC {efac} has no TOAs")
diff --git a/src/pint/models/timing_model.py b/src/pint/models/timing_model.py
index a0b27b090..68fe886bf 100644
--- a/src/pint/models/timing_model.py
+++ b/src/pint/models/timing_model.py
@@ -3425,6 +3425,7 @@ def add_param(self, param, deriv_func=None, setup=False):
         if deriv_func is not None:
             self.register_deriv_funcs(deriv_func, param.name)
         param._parent = self
+        return param.name
 
     def remove_param(self, param):
         """Remove a parameter from the Component.