High-pressure direct-injection (HPDI) in heavy duty engines allows a natural gas (NG) engine to maintain diesel-like performance while deriving most of its power from NG. A small diesel pilot injection (5-10% of the fuel energy) is used to ignite the direct injected gas jet. The NG burns in a predominantly mixing-controlled combustion mode which can produce particulate matter (PM). Here we study the effect of injection strategies on emissions from a HPDI engine in two parts. Part-I investigated the effect of late post injection (LPI); the current paper (Part-II) reports on the effects of slightly premixed combustion (SPC) on emission and engine performance. In SPC operation, the diesel injection is delayed, allowing more premixing of the natural gas prior to ignition. PM reductions and tradeoffs involved with gas slightly premixed combustion was investigated in a single-cylinder version of a 6-cylinder, 15 liter HPDI engine. SPC operation at a high-load point reduces over 90% of the PM with a 2% improvement in fuel efficiency while having almost the same level of NOx and methane. The drawback of SPC is cycle-to-cycle variation and high pressure rise rate. PM does not increase for SPC with higher EGR level, higher EQR (global oxygen based equivalence ratio) or higher pilot mass, which normally increases PM in normal (mixing-controlled) HPDI combustion. Computational Fluid Dynamics (CFD) simulation of mixing-controlled HPDI combustion showed that at the gas ignition time, there is much fuel in the rich (sooting) stoichiometry, while for SPC, the mass of fuel in the rich zone is less than 10% of the mixing-controlled HPDI combustion, and therefore the potential for soot formation is mainly eliminated. The relative timing of ignition, or peak apparent heat release rate (AHRR), and end of injection is important for the HPDI engine and it can be used to define the SPC thresholds in future. The morphology of particles produced by SPC is similar to that from conventional HPDI (and also from diesel), but the size and number concentration are reduced.