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A famous result of Bayer and Diaconis is that the Gilbert-Shannon-Reeds (GSR) model for the riffle shuffle of n cards mixes in 3/2 log_2 n steps and that for 52 cards about 7 shuffles suffices to mix the deck. The clumpy riffle shuffle and dealer riffle shuffle are variants of the GSR shuffle that have been proposed to more realistically model how people actually shuffle cards. In these models, when a card is dropped from one hand, the conditional probability that the next card is dropped from the same hand is higher/lower than for the GSR model. We give the first analysis of clumpy and dealer riffle shuffles, proving a mixing time bound of O(log^4 n). Joint work with Johan Jonasson.