diff --git a/becquerel/core/peakfinder.py b/becquerel/core/peakfinder.py
index c3ebf82a..e3dfe7a8 100644
--- a/becquerel/core/peakfinder.py
+++ b/becquerel/core/peakfinder.py
@@ -273,7 +273,11 @@ def add_peak(self, xpeak):
                 / bw**2
             )
             if d2 >= 0:
-                raise PeakFinderError("Second derivative must be negative at peak")
+                warnings.warn(
+                    f"Second derivative must be negative at peakposition {xbin}",
+                    PeakFinderWarning,
+                )
+                return
             d2 *= -1
             fwhm = 2 * np.sqrt(self.snr[xbin] / d2)
             # add the peak if it has a similar FWHM to the kernel's FWHM