Black holes with two charges in string theory are singular due to vanishing horizon area at extremality. Two seemingly contradictory resolutions are available in the literature. On one hand, it has been argued that higher-derivative effects create a string-sized extremal horizon.
On the other hand, it has been argued that before such a small black hole even forms, there is a transition to a winding condensate and eventually a gas of strings. We show that, with some modifications, these two perspectives are compatible, but correspond to different observables.
A rotating non-extremal black hole solution with higher-derivative corrections contributes to the gravitational path integral for the index,
while the transition to the gas of strings happens for the thermal partition function. Along the way, we extend the recently developed ``new attractor mechanism" by incorporating higher-derivative corrections. We also use effective theory to rule out the possibility of a string-size black hole as the correct description of the near-extremal microstates.