Recently reported miniature configurations with semiconductor distributed feedback lasers under resonant feedback are considered theoretically. Limiting instabilities and bifurcations are systematically explored by combining the theory of chirp reduction and a bifurcation analysis. It is shown that the regime of optimal chirp reduction also exhibits the best local stability. It suffers only from undamping of relaxation oscillations in a finite interval of feedback strength. The existence of a separate strong-feedback regime with high stability is consistent with the two experiments available so far. We regard this feature as a generic specificum of miniature configurations not known from large-scale setups. This regime can open new prospects for applications of compact frequency-stabilized semiconductor lasers with extremely low noise and small line width.