A MIMO keyhole is a propagation environment such that the channel gain matrix has unit rank (single degree of freedom), irrespective of the number of deployed antennas or their correlations (spacing), thereby reducing the MIMO channel capacity to that of a SISO channel. Related literature seems to consider such degeneration hopeless. Contrary to this general belief, this paper demonstrates that cooperative diversity can mitigate keyhole effects. Precisely, provided that the source-relay channel is keyhole-free, we show that there exists a ``cutoff'' relay transmit power above which keyhole effects can be mitigated even when both the source-destination and the relay-destination channels incur keyhole effect. Furthermore, assuming Rayleigh fading, the devised closed form of this power threshold is found to be independent of the channel gain matrices, thereby applying to situations where channel state information (CSI) is unreliable or unavailable at the transmitters. Numerical examples confirm the relevance of our claims.