We apply the techniques introduced by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to prove security of quantum-key-distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes. For instance, for the six-state protocol using two-way classical post-processing we recover the known threshold for the maximum tolerated bit error rate of the channel, 0.276, but demonstrate that the secret-key rate can be substantially higher than previously shown. Moreover, we provide a detailed analysis of the Bennett-Brassard 1984 (BB84) and the SARG protocol using weak coherent pulses (with and without decoy states) in the so-called untrusted-device scenario, where the adversary might influence the detector efficiencies. We evaluate lower bounds on the secret-key rate for realistic channel parameters and show that, for channels with low noise level, the bounds for the SARG protocol are superior to those for the BB84 protocol, whereas this advantage disappears with increasing noise level.