How do I deal with postdoc acceptances that come in before my preferred institution makes its decision known? I will graduate soon from the doctoral program. I will apply for multiple postdoc positions. The results of the one that I really think is great for my career will be probably announced later than the others. If I accept an earlier offer, and later learn that I could also get the one I desire the most, then I will really regret. However, I don't want to risk by refusing an early offer, since at the end I may get nothing.

Do you have any recommendations for such situations? Have you ever experienced this dilemma? How did you manage it?
This can be difficult. If you get an offer with an uncomfortable deadline, I would recommend bringing it to the attention of departments which you prefer (and/or individual faculty at those departments).

This is not guaranteed to push them to make a faster decision, but it could.