diff --git a/CHANGELOG-unreleased.md b/CHANGELOG-unreleased.md
index b4390548c..a9e07480b 100644
--- a/CHANGELOG-unreleased.md
+++ b/CHANGELOG-unreleased.md
@@ -12,6 +12,7 @@ the released changes.
 - Third-order Roemer delay terms to ELL1 model
 - Made the addition of a TZR TOA (`AbsPhase`) in the `TimingModel` explicit in `Residuals` class.
 - Updated `CONTRIBUTING.rst` with the latest information.
+- Made `TimingModel.params` and `TimingModel.ordered_params` identical. Deprecated `TimingModel.ordered_params`.
 ### Added
 - Third-order Roemer delay terms to ELL1 model
 - Options to add a TZR TOA (`AbsPhase`) during the creation of a `TimingModel` using `ModelBuilder.__call__`, `get_model`, and `get_model_and_toas`
diff --git a/src/pint/fitter.py b/src/pint/fitter.py
index 844d15db9..22e9860b3 100644
--- a/src/pint/fitter.py
+++ b/src/pint/fitter.py
@@ -363,7 +363,7 @@ def get_summary(self, nodmx=False):
 
         # to handle all parameter names, determine the longest length for the first column
         longestName = 0  # optionally specify the minimum length here instead of 0
-        for pn in self.model.params_ordered:
+        for pn in self.model.params:
             if nodmx and pn.startswith("DMX"):
                 continue
             if len(pn) > longestName:
@@ -378,7 +378,7 @@ def get_summary(self, nodmx=False):
         s += ("{:<" + spacingName + "s} {:>20s} {:>28s} {}\n").format(
             "=" * longestName, "=" * 20, "=" * 28, "=" * 5
         )
-        for pn in self.model.params_ordered:
+        for pn in self.model.params:
             if nodmx and pn.startswith("DMX"):
                 continue
             prefitpar = getattr(self.model_init, pn)
diff --git a/src/pint/models/timing_model.py b/src/pint/models/timing_model.py
index a7916da85..1bd05bfa2 100644
--- a/src/pint/models/timing_model.py
+++ b/src/pint/models/timing_model.py
@@ -183,12 +183,11 @@ class TimingModel:
     removed with methods on this object, and for many of them additional
     parameters in families (``DMXEP_1234``) can be added.
 
-    Parameters in a TimingModel object are listed in the ``model.params`` and
-    ``model.params_ordered`` objects. Each Parameter can be set as free or
-    frozen using its ``.frozen`` attribute, and a list of the free parameters
-    is available through the ``model.free_params`` property; this can also
-    be used to set which parameters are free. Several methods are available
-    to get and set some or all parameters in the forms of dictionaries.
+    Parameters in a TimingModel object are listed in the ``model.params`` object.
+    Each Parameter can be set as free or frozen using its ``.frozen`` attribute,
+    and a list of the free parameters is available through the ``model.free_params``
+    property; this can also be used to set which parameters are free. Several methods
+    are available to get and set some or all parameters in the forms of dictionaries.
 
     TimingModel objects also support a number of functions for computing
     various things like orbital phase, and barycentric versions of TOAs,
@@ -500,20 +499,30 @@ def __getattr__(self, name):
         )
 
     @property_exists
-    def params(self):
-        """List of all parameter names in this model and all its components (order is arbitrary)."""
-        # FIXME: any reason not to just use params_ordered here?
-        p = self.top_level_params
-        for cp in self.components.values():
-            p = p + cp.params
-        return p
+    def params_ordered(self):
+        """List of all parameter names in this model and all its components.
+        This is the same as `params`."""
+
+        # Historically, this was different from `params` because Python
+        # dictionaries were unordered until Python 3.7. Now there is no reason for
+        # them to be different.
+
+        warn(
+            "`TimingModel.params_ordered` is now deprecated and may be removed in the future. "
+            "Use `TimingModel.params` instead. It gives the same output as `TimingModel.params_ordered`.",
+            DeprecationWarning,
+        )
+
+        return self.params
 
     @property_exists
-    def params_ordered(self):
+    def params(self):
         """List of all parameter names in this model and all its components, in a sensible order."""
+
         # Define the order of components in the list
         # Any not included will be printed between the first and last set.
         # FIXME: make order completely canonical (sort components by name?)
+
         start_order = ["astrometry", "spindown", "dispersion"]
         last_order = ["jump_delay"]
         compdict = self.get_components_by_category()
@@ -551,7 +560,7 @@ def params_ordered(self):
     def free_params(self):
         """List of all the free parameters in the timing model. Can be set to change which are free.
 
-        These are ordered as ``self.params_ordered`` does.
+        These are ordered as ``self.params`` does.
 
         Upon setting, order does not matter, and aliases are accepted.
         ValueError is raised if a parameter is not recognized.
@@ -559,7 +568,7 @@ def free_params(self):
         On setting, parameter aliases are converted with
         :func:`pint.models.timing_model.TimingModel.match_param_aliases`.
         """
-        return [p for p in self.params_ordered if not getattr(self, p).frozen]
+        return [p for p in self.params if not getattr(self, p).frozen]
 
     @free_params.setter
     def free_params(self, params):
@@ -620,7 +629,7 @@ def get_params_dict(self, which="free", kind="quantity"):
         if which == "free":
             ps = self.free_params
         elif which == "all":
-            ps = self.params_ordered
+            ps = self.params
         else:
             raise ValueError("get_params_dict expects which to be 'all' or 'free'")
         c = OrderedDict()
@@ -2013,10 +2022,7 @@ def compare(
             log.debug("Check verbosity - only warnings/info will be displayed")
         othermodel = copy.deepcopy(othermodel)
 
-        if (
-            "POSEPOCH" in self.params_ordered
-            and "POSEPOCH" in othermodel.params_ordered
-        ):
+        if "POSEPOCH" in self.params and "POSEPOCH" in othermodel.params:
             if (
                 self.POSEPOCH.value is not None
                 and othermodel.POSEPOCH.value is not None
@@ -2027,7 +2033,7 @@ def compare(
                     % (other_model_name, model_name)
                 )
                 othermodel.change_posepoch(self.POSEPOCH.value)
-        if "PEPOCH" in self.params_ordered and "PEPOCH" in othermodel.params_ordered:
+        if "PEPOCH" in self.params and "PEPOCH" in othermodel.params:
             if (
                 self.PEPOCH.value is not None
                 and self.PEPOCH.value != othermodel.PEPOCH.value
@@ -2036,7 +2042,7 @@ def compare(
                     "Updating PEPOCH in %s to match %s" % (other_model_name, model_name)
                 )
                 othermodel.change_pepoch(self.PEPOCH.value)
-        if "DMEPOCH" in self.params_ordered and "DMEPOCH" in othermodel.params_ordered:
+        if "DMEPOCH" in self.params and "DMEPOCH" in othermodel.params:
             if (
                 self.DMEPOCH.value is not None
                 and self.DMEPOCH.value != othermodel.DMEPOCH.value
@@ -2071,7 +2077,7 @@ def compare(
                     f"{model_name} is in ECL({self.ECL.value}) coordinates but {other_model_name} is in ICRS coordinates and convertcoordinates=False"
                 )
 
-        for pn in self.params_ordered:
+        for pn in self.params:
             par = getattr(self, pn)
             if par.value is None:
                 continue
@@ -2298,8 +2304,8 @@ def compare(
                 )
 
         # Now print any parameters in othermodel that were missing in self.
-        mypn = self.params_ordered
-        for opn in othermodel.params_ordered:
+        mypn = self.params
+        for opn in othermodel.params:
             if opn in mypn and getattr(self, opn).value is not None:
                 continue
             if nodmx and opn.startswith("DMX"):
diff --git a/tests/test_design_matrix.py b/tests/test_design_matrix.py
index 0b5e06e6e..443888015 100644
--- a/tests/test_design_matrix.py
+++ b/tests/test_design_matrix.py
@@ -110,3 +110,8 @@ def test_combine_designmatrix_all(self):
             ]
             == 0.0
         )
+
+    def test_param_order(self):
+        params_dm = self.model.designmatrix(self.toas, incoffset=False)[1]
+        params_free = self.model.free_params
+        assert params_dm == params_free