Despite evidence that wind conditions are an important factor in determining stopover decisions, models of time-minimizing bird migration have up to now emphasized the optimal response of the migrants to variations in fuel acquisition rates. We present a simple model of a time-minimizing migrant faced with two potential wind conditions on each day, which occur with a fixed probability. Wind assistance is modelled as a multiplicative factor in the flight range equation. We identify conditions under which birds leave the stopover site even with no tailwinds and conditions where the birds leave only with tailwinds in cases with global and local variation of the fuel deposition rate. The optimal policy depends on the probability and amount of wind assistance. In all cases there is an initial period at a stopover site when the bird should stay and build up its initially small fuel reserves irrespective of wind. After this initial time, there is a period when the optimal departure decision is to leave when tailwinds occur but stay and continue fuel deposition in other winds. If the probability of tailwinds is low the bird should at some later time change its policy to leave even in unfavourable winds. However, if a certain threshold value of the probability of favourable winds is reached the birds should never leave without wind assistance. These patterns lead to a complex relationship between departure load and fuel deposition rate. We compare our predictions with a null-model where the birds simply leave as soon as favourable winds occur. We further show that the inclusion of wind assistance cannot explain the discrepancy between observed and predicted values of departure loads under local variation in fuelling rates.