K.O.
Ok, you're going to hate this but.... He's 4 months old, the vast majority of babies this age are irregular sleepers. No, you shouldn't just let him fuss at night. If a baby this age cries at night you should go and comfort him. It isn't until 6 months of age that experts suggest you allow the baby to fuss and learn to self soothe. At 4 months when baby wakes up you go and provide comfort and whatever else the baby needs until they go back to sleep. The best way to get him to sleep, in my opinion, is just to provide minimal interaction and comfort that way your aren't encouraging him to call you in for visits. The less you have to offer the less likely he is to fuss for you. But you can't expect much from a 4 month old.