Periodically fluctuating environments occur in various ways in nature but have not, however, been studied in detail yet in the context of the color of environmental noise and extinction risk of populations. We use a stochastic model to simulate population dynamics with compensatory density regulation under four different patterns of periodically fluctuating environments. We found that extinction risk changes dramatically from what was known if the underlying environmental stochasticity driving population dynamics is periodically correlated rather than randomly correlated. Fluctuating environments with a very short period are found to decrease extinction risk over "white noise" fluctuations because a species is never in a bad environment for too long. Conversely. long periods increase extinction risk because species accumulate too much time in a bad environment. Moreover, we found the mean, variance, frequency distribution and especially the extensively studied noise color not to be sufficient for predicting extinction risk in periodically fluctuating environments. Rather, additional attributes of environmental noise have to be considered. The occurrence of monotonic trends within time series of environmental data (e.g. after 'disturbance' events), in combination with density regulation, may also affect extinction risk. Our study exemplifies that the investigation of periodically fluctuating environments leads to new insights into the interaction between environmental variation, population dynamics and the resulting extinction risk.