diff --git a/doc/api/next_api_changes/deprecations.rst b/doc/api/next_api_changes/deprecations.rst
index 9e9fc0a6f40e..d33d6d643908 100644
--- a/doc/api/next_api_changes/deprecations.rst
+++ b/doc/api/next_api_changes/deprecations.rst
@@ -242,3 +242,8 @@ The following related APIs are also deprecated:
 ``matplotlib.test(recursionlimit=...)``
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 The *recursionlimit* parameter of ``matplotlib.test`` is deprecated.
+
+mathtext glues
+~~~~~~~~~~~~~~
+The *copy* parameter of ``mathtext.Glue`` is deprecated (the underlying glue
+spec is now immutable).  ``mathtext.GlueSpec`` is deprecated.
diff --git a/lib/matplotlib/mathtext.py b/lib/matplotlib/mathtext.py
index ccd033850de8..d05241aef528 100644
--- a/lib/matplotlib/mathtext.py
+++ b/lib/matplotlib/mathtext.py
@@ -1849,41 +1849,57 @@ def __init__(self, state):
         Rule.__init__(self, thickness, np.inf, np.inf, state)
 
 
+_GlueSpec = namedtuple(
+    "_GlueSpec", "width stretch stretch_order shrink shrink_order")
+_GlueSpec._named = {
+    'fil':         _GlueSpec(0., 1., 1, 0., 0),
+    'fill':        _GlueSpec(0., 1., 2, 0., 0),
+    'filll':       _GlueSpec(0., 1., 3, 0., 0),
+    'neg_fil':     _GlueSpec(0., 0., 0, 1., 1),
+    'neg_fill':    _GlueSpec(0., 0., 0, 1., 2),
+    'neg_filll':   _GlueSpec(0., 0., 0, 1., 3),
+    'empty':       _GlueSpec(0., 0., 0, 0., 0),
+    'ss':          _GlueSpec(0., 1., 1, -1., 1),
+}
+
+
 class Glue(Node):
     """
     Most of the information in this object is stored in the underlying
-    `GlueSpec` class, which is shared between multiple glue objects.
+    ``_GlueSpec`` class, which is shared between multiple glue objects.
     (This is a memory optimization which probably doesn't matter anymore, but
     it's easier to stick to what TeX does.)
     """
 
+    @cbook.deprecated("3.3")
+    @property
+    def glue_subtype(self):
+        return "normal"
+
+    @cbook._delete_parameter("3.3", "copy")
     def __init__(self, glue_type, copy=False):
         Node.__init__(self)
-        self.glue_subtype   = 'normal'
         if isinstance(glue_type, str):
-            glue_spec = GlueSpec.factory(glue_type)
-        elif isinstance(glue_type, GlueSpec):
+            glue_spec = _GlueSpec._named[glue_type]
+        elif isinstance(glue_type, _GlueSpec):
             glue_spec = glue_type
         else:
             raise ValueError("glue_type must be a glue spec name or instance")
-        if copy:
-            glue_spec = glue_spec.copy()
-        self.glue_spec      = glue_spec
+        self.glue_spec = glue_spec
 
     def shrink(self):
         Node.shrink(self)
         if self.size < NUM_SIZE_LEVELS:
-            if self.glue_spec.width != 0.:
-                self.glue_spec = self.glue_spec.copy()
-                self.glue_spec.width *= SHRINK_FACTOR
+            g = self.glue_spec
+            self.glue_spec = g._replace(width=g.width * SHRINK_FACTOR)
 
     def grow(self):
         Node.grow(self)
-        if self.glue_spec.width != 0.:
-            self.glue_spec = self.glue_spec.copy()
-            self.glue_spec.width *= GROW_FACTOR
+        g = self.glue_spec
+        self.glue_spec = g._replace(width=g.width * GROW_FACTOR)
 
 
+@cbook.deprecated("3.3")
 class GlueSpec:
     """See `Glue`."""
 
@@ -1908,16 +1924,9 @@ def factory(cls, glue_type):
         return cls._types[glue_type]
 
 
-GlueSpec._types = {
-    'fil':         GlueSpec(0., 1., 1, 0., 0),
-    'fill':        GlueSpec(0., 1., 2, 0., 0),
-    'filll':       GlueSpec(0., 1., 3, 0., 0),
-    'neg_fil':     GlueSpec(0., 0., 0, 1., 1),
-    'neg_fill':    GlueSpec(0., 0., 0, 1., 2),
-    'neg_filll':   GlueSpec(0., 0., 0, 1., 3),
-    'empty':       GlueSpec(0., 0., 0, 0., 0),
-    'ss':          GlueSpec(0., 1., 1, -1., 1)
-}
+with cbook._suppress_matplotlib_deprecation_warning():
+    GlueSpec._types = {k: GlueSpec(**v._asdict())
+                       for k, v in _GlueSpec._named.items()}
 
 
 # Some convenient ways to get common kinds of glue