diff --git a/README.rst b/README.rst
index 5acc5279..5e28cce7 100644
--- a/README.rst
+++ b/README.rst
@@ -2,7 +2,7 @@
 anesthetic: nested sampling post-processing
 ===========================================
 :Authors: Will Handley and Lukas Hergt
-:Version: 2.8.15
+:Version: 2.8.16
 :Homepage: https://github.com/handley-lab/anesthetic
 :Documentation: http://anesthetic.readthedocs.io/
 
diff --git a/anesthetic/_version.py b/anesthetic/_version.py
index 7cdefb37..f8f5d150 100644
--- a/anesthetic/_version.py
+++ b/anesthetic/_version.py
@@ -1 +1 @@
-__version__ = '2.8.15'
+__version__ = '2.8.16'
diff --git a/anesthetic/samples.py b/anesthetic/samples.py
index d0dee2b1..44c81076 100644
--- a/anesthetic/samples.py
+++ b/anesthetic/samples.py
@@ -1302,15 +1302,17 @@ def recompute(self, logL_birth=None, inplace=False):
             n_bad = invalid.sum()
             n_equal = (samples.logL == samples.logL_birth).sum()
             if n_bad:
-                warnings.warn("%i out of %i samples have logL <= logL_birth,"
-                              "\n%i of which have logL == logL_birth."
-                              "\nThis may just indicate numerical rounding "
-                              "errors at the peak of the likelihood, but "
-                              "further investigation of the chains files is "
-                              "recommended."
-                              "\nDropping the invalid samples." %
-                              (n_bad, len(samples), n_equal),
-                              RuntimeWarning)
+                n_inf = ((samples.logL == samples.logL_birth) &
+                         (samples.logL == -np.inf)).sum()
+                if n_bad > n_inf:
+                    warnings.warn(
+                        "%i out of %i samples have logL <= logL_birth,\n"
+                        "%i of which have logL == logL_birth.\n"
+                        "This may just indicate numerical rounding errors at "
+                        "the peak of the likelihood, but further "
+                        "investigation of the chains files is recommended.\n"
+                        "Dropping the invalid samples."
+                        % (n_bad, len(samples), n_equal), RuntimeWarning)
                 samples = samples[~invalid].reset_index(drop=True)
 
             samples.sort_values('logL', inplace=True)
diff --git a/tests/test_samples.py b/tests/test_samples.py
index f49aed3d..0dfdf4c8 100644
--- a/tests/test_samples.py
+++ b/tests/test_samples.py
@@ -1133,6 +1133,7 @@ def test_beta():
 def test_beta_with_logL_infinities():
     ns = read_chains("./tests/example_data/pc")
     ns.loc[:10, ('logL', r'$\ln\mathcal{L}$')] = -np.inf
+    ns.loc[1000, ('logL', r'$\ln\mathcal{L}$')] = -np.inf
     with pytest.warns(RuntimeWarning):
         ns.recompute(inplace=True)
     assert (ns.logL == -np.inf).sum() == 0