Applicants have disclosed an improved trigger assembly for firearms, and a related method, to avoid premature firing after an unintentional trigger pull, especially where light trigger pulls have previously been set. In the preferred embodiment, Applicants' trigger assembly has two non-coaxial triggers: a slotted primary trigger and a secondary trigger which can pivot into the slot. During an intentional trigger pull, the shooter's finger initially pushes against the secondary trigger until it pivots and nestles within the primary trigger's slot. Continued pulling on both the secondary and primary triggers causes a sear to fall off the primary trigger and the firearm to discharge. In an unintentional trigger pull, where the secondary trigger is not pulled back enough to nestle within the primary trigger's slot, a protrusion on the secondary trigger blocks the sear from falling, thereby avoiding discharge.