diff --git a/.github/workflows/test_branches.yml b/.github/workflows/test_branches.yml
index 7b0e9843981..26026eace8b 100644
--- a/.github/workflows/test_branches.yml
+++ b/.github/workflows/test_branches.yml
@@ -304,7 +304,14 @@ jobs:
         python -m pip install --cache-dir cache/pip pymysql || \
             python -m pip install --cache-dir cache/pip pymysql
         if test -z "${{matrix.slim}}"; then
-            python -m pip install --cache-dir cache/pip 'cplex!=22.1.2.1' docplex \
+            # Disallow cplex 22.1.2.1 because it errors fatally when
+            #  computing IIS on python 3.13 and 3.14
+            if [[ ${{matrix.python}} =~ 3.1[34] ]]; then
+                CPLEX='cplex!=22.1.2.1'
+            else
+                CPLEX='cplex'
+            fi
+            python -m pip install --cache-dir cache/pip "$CPLEX" docplex \
                 || echo "WARNING: CPLEX Community Edition is not available"
             python -m pip install --cache-dir cache/pip gurobipy \
                 || echo "WARNING: Gurobi is not available"
@@ -375,6 +382,18 @@ jobs:
         # possibly if it outputs messages to stderr)
         conda install --update-deps -q -y python="${{matrix.python}}" $CONDA_DEPENDENCIES
         if test -z "${{matrix.slim}}"; then
+            TIMEOUT_MSG="TIMEOUT: killing conda install process"
+            PYVER=$(echo "py${{matrix.python}}" | sed 's/\.//g')
+            echo "Installing for $PYVER"
+            #
+            # Disallow cplex 22.1.2 and 22.1.2.1, as they error fatally when
+            #   computing IIS on Python 3.13 and 3.14
+            # Disallow cplex 12.9 (caused segfaults in tests)
+            if [[ ${{matrix.python}} =~ 3.1[34] ]]; then
+                CPLEX='cplex>=12.10,<22.1.2|>22.1.2.1'
+            else
+                CPLEX='cplex>=12.10'
+            fi
             # xpress.init() (xpress 9.5.1 from conda) hangs indefinitely
             # on GHA/Windows under Python 3.10 and 3.11.  Exclude that
             # release on that platform.
@@ -387,10 +406,7 @@ jobs:
             else
                 XPRESS='xpress'
             fi
-            TIMEOUT_MSG="TIMEOUT: killing conda install process"
-            PYVER=$(echo "py${{matrix.python}}" | sed 's/\.//g')
-            echo "Installing for $PYVER"
-            for PKG in 'cplex>=12.10' docplex gurobi "$XPRESS" cyipopt pymumps scip; do
+            for PKG in "$CPLEX" docplex gurobi "$XPRESS" cyipopt pymumps scip; do
                 echo ""
                 echo "*** Install $PKG ***"
                 echo ""
diff --git a/.github/workflows/test_pr_and_main.yml b/.github/workflows/test_pr_and_main.yml
index c14d52bb316..32663db656a 100644
--- a/.github/workflows/test_pr_and_main.yml
+++ b/.github/workflows/test_pr_and_main.yml
@@ -356,7 +356,14 @@ jobs:
         python -m pip install --cache-dir cache/pip pymysql || \
             python -m pip install --cache-dir cache/pip pymysql
         if test -z "${{matrix.slim}}"; then
-            python -m pip install --cache-dir cache/pip 'cplex!=22.1.2.1' docplex \
+            # Disallow cplex 22.1.2.1 because it errors fatally when
+            #  computing IIS on python 3.13 and 3.14
+            if [[ ${{matrix.python}} =~ 3.1[34] ]]; then
+                CPLEX='cplex!=22.1.2.1'
+            else
+                CPLEX='cplex'
+            fi
+            python -m pip install --cache-dir cache/pip "$CPLEX" docplex \
                 || echo "WARNING: CPLEX Community Edition is not available"
             python -m pip install --cache-dir cache/pip gurobipy \
                 || echo "WARNING: Gurobi is not available"
@@ -427,6 +434,18 @@ jobs:
         # possibly if it outputs messages to stderr)
         conda install --update-deps -q -y python="${{matrix.python}}" $CONDA_DEPENDENCIES
         if test -z "${{matrix.slim}}"; then
+            TIMEOUT_MSG="TIMEOUT: killing conda install process"
+            PYVER=$(echo "py${{matrix.python}}" | sed 's/\.//g')
+            echo "Installing for $PYVER"
+            #
+            # Disallow cplex 22.1.2 and 22.1.2.1, as they error fatally when
+            #   computing IIS on Python 3.13 and 3.14
+            # Disallow cplex 12.9 (caused segfaults in tests)
+            if [[ ${{matrix.python}} =~ 3.1[34] ]]; then
+                CPLEX='cplex>=12.10,<22.1.2|>22.1.2.1'
+            else
+                CPLEX='cplex>=12.10'
+            fi
             # xpress.init() (xpress 9.5.1 from conda) hangs indefinitely
             # on GHA/Windows under Python 3.10 and 3.11.  Exclude that
             # release on that platform.
@@ -439,10 +458,7 @@ jobs:
             else
                 XPRESS='xpress'
             fi
-            TIMEOUT_MSG="TIMEOUT: killing conda install process"
-            PYVER=$(echo "py${{matrix.python}}" | sed 's/\.//g')
-            echo "Installing for $PYVER"
-            for PKG in 'cplex>=12.10' docplex gurobi "$XPRESS" cyipopt pymumps scip; do
+            for PKG in "$CPLEX" docplex gurobi "$XPRESS" cyipopt pymumps scip; do
                 echo ""
                 echo "*** Install $PKG ***"
                 echo ""