Photoluminescence (PL) spectra of atomically thin 2D lead iodide perovskite films are shown to depend on excited-state density, especially at cryogenic temperatures. At high excited-state densities and low temperatures, free exciton (FE) emission is so suppressed by exciton-exciton annihilation (EEA) that other-normally much weaker-emissions dominate the PL spectrum, such as emission from bound excitons (BEs) or PbI

2 inclusions. In the Ruddlesden-Popper perovskite with phenethylammonium (PEA) ligands (PEA

2PbI

4, PEPI), FE emission dominates at all temperatures at the excited-state densities reached with continuous wave excitation. At higher excited state densities reached with femtosecond pulsed excitation, the PL at temperatures under 100K is dominated by BE emission redshifted from that of FE by 40.3meV. Weak emission from PbI

2 inclusions 170meV higher in energy than FE PL is also observable under these conditions. Equilibrium between BE and FE states explains why FE emission first increases with decreasing temperature from 290 until 140K and then decreases with decreasing temperature as the BEs become stable. A Dion-Jacobson (DJ) material based on 1,4-phenyl-enedimethanammonium (PDMA) supports the reduction of FE emission by EEA at cryogenic temperatures. However, in the PDMA-based DJ material, BE emission is never as pronounced. At low temperatures and high-excited state densities caused by pulsed excitation, a broad emission redshifted by 390meV from the FE dominates. Based on comparison with temperature-dependent measurements of PbI

2 films, this emission is suggested to arise from PbI

2 inclusions in the material. Possible avenues for improving PL at room temperature are discussed concerning these findings.