diff --git a/control/pzmap.py b/control/pzmap.py
index a1f71da1f..d7662d1d9 100644
--- a/control/pzmap.py
+++ b/control/pzmap.py
@@ -330,7 +330,7 @@ def pole_zero_plot(
             if grid == 'empty':
                 # Leave off grid entirely
                 ax = plt.axes()
-                xlim = ylim = [0, 0]    # use data to set limits
+                xlim = ylim = [np.inf, -np.inf] # use data to set limits
             else:
                 # draw stability boundary; use first response timebase
                 ax, fig = nogrid(data[0].dt, scaling=scaling)
@@ -574,7 +574,7 @@ def _compute_root_locus_limits(response):
         ]
         ylim = max(0, np.max(response.sys.zeros().imag))
     else:
-        xlim, ylim = [0, 0], 0
+        xlim, ylim = [np.inf, -np.inf], 0
 
     # Go through each locus and look for features
     rho = config._get_param('pzmap', 'buffer_factor')
@@ -603,6 +603,12 @@ def _compute_root_locus_limits(response):
         xlim[1] = rho * xlim[1] if xlim[1] > 0 else 0
         ylim = rho * ylim if ylim > 0 else np.max(np.abs(xlim))
 
+    # Make sure the limits make sense
+    if xlim == [0, 0]:
+        xlim = [-1, 1]
+    if ylim == 0:
+        ylim = 1
+
     return xlim, [-ylim, ylim]
 
 
diff --git a/control/tests/rlocus_test.py b/control/tests/rlocus_test.py
index 5ee2830c9..5511f5b82 100644
--- a/control/tests/rlocus_test.py
+++ b/control/tests/rlocus_test.py
@@ -186,11 +186,13 @@ def test_root_locus_documentation(savefigs=False):
     sys = ct.tf([1, 2], [1, 2, 3], name='SISO transfer function')
     response = ct.pole_zero_map(sys)
     ct.pole_zero_plot(response)
-    plt.savefig('pzmap-siso_ctime-default.png')
+    if savefigs:
+        plt.savefig('pzmap-siso_ctime-default.png')
 
     plt.figure()
     ct.root_locus_map(sys).plot()
-    plt.savefig('rlocus-siso_ctime-default.png')
+    if savefigs:
+        plt.savefig('rlocus-siso_ctime-default.png')
 
     # TODO: generate event in order to generate real title
     plt.figure()
@@ -200,18 +202,21 @@ def test_root_locus_documentation(savefigs=False):
     with plt.rc_context(freqplot_rcParams):
         ax.set_title(
             "Clicked at: -2.729+1.511j  gain = 3.506  damping = 0.8748")
-    plt.savefig('rlocus-siso_ctime-clicked.png')
+    if savefigs:
+        plt.savefig('rlocus-siso_ctime-clicked.png')
 
     plt.figure()
     sysd = sys.sample(0.1)
     ct.root_locus_plot(sysd)
-    plt.savefig('rlocus-siso_dtime-default.png')
+    if savefigs:
+        plt.savefig('rlocus-siso_dtime-default.png')
 
     plt.figure()
     sys1 = ct.tf([1, 2], [1, 2, 3], name='sys1')
     sys2 = ct.tf([1, 0.2], [1, 1, 3, 1, 1], name='sys2')
     ct.root_locus_plot([sys1, sys2], grid=False)
-    plt.savefig('rlocus-siso_multiple-nogrid.png')
+    if savefigs:
+        plt.savefig('rlocus-siso_multiple-nogrid.png')
 
 
 if __name__ == "__main__":