The security of quantum key distribution (QKD) has been proven for different protocols, in particular for the BB84 protocol. It has been shown that this scheme is robust against eventual imperfections in the state preparation, and sending only three different states delivers the same secret key rate achievable with four states. In this work, we prove in a finite-key scenario that the security of this protocol can be maintained even with fewer measurement operators on the receiver. This allows us to implement a time-bin encoding scheme with a minimum amount of resources.