An exemplary damper module is configured for use with a latchbolt assembly, and generally includes a mounting bracket, a first slowing mechanism, and a second slowing mechanism. The latchbolt assembly generally includes a drive member, a latchbolt, and a retractor connected between the drive member and the latchbolt. Each of the slowing mechanisms is independently operable to slow the extension speed of the latchbolt. The first slowing mechanism includes a rack gear and a rotary damper including a pinion gear. The rack gear is configured to be mounted to the drive member, and the rotary damper is mounted to the mounting bracket. The second slowing mechanism includes a slowing arm and a biasing member engaged with the slowing arm. The slowing arm is movably mounted to the mounting bracket and is configured to engage the retractor.