Many works have studied the negative impact of slow start on the performance of short transfers. Some works propose to accelerate the window increase during this phase in order to improve the performance especially on satellite links. Others propose to set the slow start threshold at the beginning of the connection to a more accurate value in order to avoid losses. But, these works didn't account for the impact of network buffers on the performance. It is known that small buffers along with a fast window increase leads to an early buffer overflow and an underestimation of the network capacity. This may change completely the performance predicted by these modifications. In this paper, we present a general analysis of this first phase as a function of all the possible parameters. We show that, as claimed, the previous works improve the performance on paths with large buffers. However, on paths with small buffers, completely different results could be obtained.