diff --git a/CIME/SystemTests/eri.py b/CIME/SystemTests/eri.py
index fdd02455987..f0a237b6819 100644
--- a/CIME/SystemTests/eri.py
+++ b/CIME/SystemTests/eri.py
@@ -272,7 +272,7 @@ def run_phase(self):
 
         self._skip_pnl = False
         # run branch case (short term archiving is off)
-        self.run_indv()
+        self.run_indv(suffix="branch")
 
         #
         # (3b) Test run:
@@ -302,5 +302,17 @@ def run_phase(self):
         # do the restart run (short term archiving is off)
         self.run_indv(suffix="rest")
 
-        self._component_compare_test("base", "hybrid")
-        self._component_compare_test("base", "rest")
+        # Note that, for both of these comparisons, the "test" case comes first and the
+        # "control" case comes second: the branch case is compared against the hybrid case
+        # (which it branched off of, and so serves as its "control"); the "rest" run is a
+        # restart from the branch case and so is compared against this branch case. We
+        # make this choice because the cprnc output file names are derived from the first
+        # suffix, so:
+        # - Listing the "test" case as the first suffix means that the cprnc files are
+        #   named with the name of the case we're testing in that cprnc comparison, which
+        #   is more intuitive.
+        # - Having the first suffix differ between the two comparisons is important to
+        #   avoid having the cprnc output files from the second comparison overwrite the
+        #   files from the first comparison.
+        self._component_compare_test("branch", "hybrid")
+        self._component_compare_test("rest", "branch")
diff --git a/doc/source/system_testing.rst b/doc/source/system_testing.rst
index 8b315405cb2..94804b2da47 100644
--- a/doc/source/system_testing.rst
+++ b/doc/source/system_testing.rst
@@ -239,14 +239,14 @@ TESTTYPE     Description
                 and writing restarts at day 10.
                 ref2case is a clone of the main case.
                 Short term archiving is on.
-              case
+              case (Suffix branch)
                 Do a branch run, starting from restarts written in ref2case,
                 for 9 days and writing restarts at day 5.
                 Short term archiving is off.
-              case (Suffix base)
+              case - restart (Suffix rest)
                 Do a restart run from the branch run restarts for 4 days.
-                Compare component history files '.base' and '.hybrid' at day 19.
                 Short term archiving is off.
+              Comparisons are done between branch vs. hybrid and rest vs. branch
 
    ERP       PES counts hybrid (OPENMP/MPI) restart bit-for-bit test from startup, (default 6 days + 5 days).
               Initial PES set up out of the box