diff --git a/gdb/ChangeLog b/gdb/ChangeLog
index b15a3a4e25f..e2d2e15b653 100644
--- a/gdb/ChangeLog
+++ b/gdb/ChangeLog
@@ -1,3 +1,14 @@
+2020-07-21  Andrew Burgess  <andrew.burgess@embecosm.com>
+
+	* python/py-registers.c (gdbpy_register_object_data): New static
+	global.
+	(gdbpy_register_object_data_init): New function.
+	(gdbpy_new_register_descriptor): Renamed to...
+	(gdbpy_get_register_descriptor): ...this, and update to reuse
+	existing register descriptors where possible.
+	(gdbpy_register_descriptor_iter_next): Update.
+	(gdbpy_initialize_registers): Register new gdbarch data.
+
 2020-07-21  Simon Marchi  <simon.marchi@efficios.com>
 
 	* linux-nat.c (stopped_pids): Make static.
diff --git a/gdb/python/py-registers.c b/gdb/python/py-registers.c
index db0fe37eecb..8e22a919d87 100644
--- a/gdb/python/py-registers.c
+++ b/gdb/python/py-registers.c
@@ -24,6 +24,9 @@
 #include "reggroups.h"
 #include "python-internal.h"
 
+/* Token to access per-gdbarch data related to register descriptors.  */
+static struct gdbarch_data *gdbpy_register_object_data = NULL;
+
 /* Structure for iterator over register descriptors.  */
 typedef struct {
   PyObject_HEAD
@@ -81,6 +84,17 @@ typedef struct {
 extern PyTypeObject reggroup_object_type
     CPYCHECKER_TYPE_OBJECT_FOR_TYPEDEF ("reggroup_object");
 
+/* Associates a vector of gdb.RegisterDescriptor objects with GDBARCH as
+   gdbarch_data via the gdbarch post init registration mechanism
+   (gdbarch_data_register_post_init).  */
+
+static void *
+gdbpy_register_object_data_init (struct gdbarch *gdbarch)
+{
+  std::vector<gdbpy_ref<>> *vec = new (std::vector<gdbpy_ref<>>);
+  return (void *) vec;
+}
+
 /* Create a new gdb.RegisterGroup object wrapping REGGROUP.  */
 
 static PyObject *
@@ -117,20 +131,38 @@ gdbpy_reggroup_name (PyObject *self, void *closure)
   return gdbpy_reggroup_to_string (self);
 }
 
-/* Create an return a new gdb.RegisterDescriptor object.  */
-static PyObject *
-gdbpy_new_register_descriptor (struct gdbarch *gdbarch,
+/* Return a gdb.RegisterDescriptor object for REGNUM from GDBARCH.  For
+   each REGNUM (in GDBARCH) only one descriptor is ever created, which is
+   then cached on the GDBARCH.  */
+
+static gdbpy_ref<>
+gdbpy_get_register_descriptor (struct gdbarch *gdbarch,
 			       int regnum)
 {
-  /* Create a new object and fill in its details.  */
-  register_descriptor_object *reg
-    = PyObject_New (register_descriptor_object,
-		    &register_descriptor_object_type);
-  if (reg == NULL)
-    return NULL;
-  reg->regnum = regnum;
-  reg->gdbarch = gdbarch;
-  return (PyObject *) reg;
+  auto vec = (std::vector<gdbpy_ref<>> *) gdbarch_data
+    (gdbarch, gdbpy_register_object_data);
+
+  /* Ensure that we have enough entries in the vector.  */
+  if (vec->size () <= regnum)
+    vec->resize ((regnum + 1), nullptr);
+
+  /* If we don't already have a descriptor for REGNUM in GDBARCH then
+     create one now.  */
+  if (vec->at (regnum) == nullptr)
+    {
+      gdbpy_ref <register_descriptor_object> reg
+	(PyObject_New (register_descriptor_object,
+		       &register_descriptor_object_type));
+      if (reg == NULL)
+	return NULL;
+      reg->regnum = regnum;
+      reg->gdbarch = gdbarch;
+      vec->at (regnum) = gdbpy_ref<> ((PyObject *) reg.release ());
+    }
+
+  /* Grab the register descriptor from the vector, the reference count is
+     automatically incremented thanks to gdbpy_ref.  */
+  return vec->at (regnum);
 }
 
 /* Convert the register descriptor to a string.  */
@@ -281,7 +313,7 @@ gdbpy_register_descriptor_iter_next (PyObject *self)
       iter_obj->regnum++;
 
       if (name != nullptr && *name != '\0')
-	return gdbpy_new_register_descriptor (gdbarch, regnum);
+	return gdbpy_get_register_descriptor (gdbarch, regnum).release ();
     }
   while (true);
 }
@@ -291,6 +323,9 @@ gdbpy_register_descriptor_iter_next (PyObject *self)
 int
 gdbpy_initialize_registers ()
 {
+  gdbpy_register_object_data
+    = gdbarch_data_register_post_init (gdbpy_register_object_data_init);
+
   register_descriptor_object_type.tp_new = PyType_GenericNew;
   if (PyType_Ready (&register_descriptor_object_type) < 0)
     return -1;
diff --git a/gdb/testsuite/ChangeLog b/gdb/testsuite/ChangeLog
index 804df0264b5..6b13e928497 100644
--- a/gdb/testsuite/ChangeLog
+++ b/gdb/testsuite/ChangeLog
@@ -1,3 +1,7 @@
+2020-07-21  Andrew Burgess  <andrew.burgess@embecosm.com>
+
+	* gdb.python/py-arch-reg-names.exp: Additional tests.
+
 2020-07-21  Tom de Vries  <tdevries@suse.de>
 
 	* gdb.reverse/solib-precsave.exp: Handle additional "recommended
diff --git a/gdb/testsuite/gdb.python/py-arch-reg-names.exp b/gdb/testsuite/gdb.python/py-arch-reg-names.exp
index 14bc0a822a4..8dd34ef5fd2 100644
--- a/gdb/testsuite/gdb.python/py-arch-reg-names.exp
+++ b/gdb/testsuite/gdb.python/py-arch-reg-names.exp
@@ -85,3 +85,22 @@ for { set i 0 } { $i < [llength $regs] } { incr i } {
     }
 }
 gdb_assert { $found_non_match == 0 } "all registers match"
+
+# Check that we get the same register descriptors from two different
+# iterators.
+gdb_py_test_silent_cmd \
+    "python iter1 = arch.registers ()" \
+    "get first all register iterator" 0
+gdb_py_test_silent_cmd \
+    "python iter2 = arch.registers ()" \
+    "get second all register iterator" 0
+gdb_py_test_silent_cmd \
+    [multi_line_input \
+	 "python" \
+	 "for r1, r2 in zip(iter1, iter2):" \
+	 "  if (r1.name != r2.name):"\
+	 "    raise gdb.GdbError (\"miss-matched names\")" \
+	 "  if (r1 != r2):" \
+	 "    raise gdb.GdbError (\"miss-matched objects\")" \
+	 "\004" ] \
+    "check names and objects match" 1