Secure Multi-Party Computation (MPC) with small number of parties is an interesting area of research, primarily due to its ability to model most real-life MPC applications and the simplicity and efficiency of the resulting protocols. In this work, we present efficient, constant-round 3-party (3PC) and 4-party (4PC) protocols in the honest-majority setting that achieve strong security notions of fairness (corrupted parties receive their output only if all honest parties receive output) and guaranteed output delivery (corrupted parties cannot prevent honest parties from receiving their output). Being constant-round, our constructions are suitable for Internet-like high-latency networks and are built from garbled circuits (GC). Assuming the minimal model of pairwise-private channels, we present two protocols that involve computation and communication of a single GC– (a) a 4-round 3PC with fairness, (b) a 5-round 4PC with guaranteed output delivery. Empirically, our protocols are on par with the best known 3PC protocol of Mohassel et al. [CCS 2015] that only achieves security with selective abort, in terms of the computation time, LAN runtime, WAN runtime and communication cost. In fact, our 4PC outperforms the 3PC of Mohassel et al. significantly in terms of per-party computation and communication cost. With an extra GC, we improve the round complexity of our 4PC to four rounds. The only 4PC in our setting, given by Ishai et al. [CRYPTO 2015], involves 12 GCs. Assuming an additional broadcast channel, we present a 5-round 3PC with guaranteed output delivery that involves computation and communication of a single GC. A broadcast channel is inevitable in this setting for achieving guaranteed output delivery, owing to an impossibility result in the literature. The overall broadcast communication of our protocol is nominal and most importantly, is independent of the circuit size. This protocol too induces a nominal overhead compared to the protocol of Mohassel et al.