diff --git a/pyfstat/core.py b/pyfstat/core.py
index 353001690437861d933c3f8a171632ebee03cba8..6ec7eb78d38dc545083c083edfa9a6d069032f3e 100755
--- a/pyfstat/core.py
+++ b/pyfstat/core.py
@@ -531,6 +531,7 @@ class ComputeFstat(object):
         """
         SFTminStartTime = self.SFT_timestamps[0]
         SFTmaxStartTime = self.SFT_timestamps[-1]
+        tstart = np.max([SFTminStartTime, tstart])
         min_tau = np.max([SFTminStartTime - tstart, 0]) + 3600*6
         max_tau = SFTmaxStartTime - tstart
         taus = np.linspace(min_tau, max_tau, npoints)