We study the spectral and dynamical behavior of two identical, mutually delay-coupled semiconductor lasers. We concentrate on the short coupling-time regime where the number of basic states of the system, the compound laser modes (CLMs), is small so that their individual behavior can be studied both experimentally and theoretically. As such it constitutes a prototype example of delay-coupled laser systems, which play an important role, e.g., in telecommunication. Specifically, for small spectral detuning we find several stable CLMs of the coupled system where both lasers lock onto a common frequency and emit continuous wave output. A bifurcation analysis of the CLMs in the full rate equation model with delay reveals the structure of stable and unstable CLMs. We find a characteristic bifurcation scenario as a function of the detuning and the coupling phase between the two lasers that explains experimentally observed multistabilities and mode jumps in the locking region.