The evolution of the coercivity H(c) and the switching field distribution (SFD) of some commercial iron particles for magnetic recording with the packing density p is analyzed. For some samples the curves H(c) vs. p show a maximum and the corresponding SFD vs. p plots have a minimum. This behavior is ascribed to the different role of the axial interactions and of the lateral interactions among the particles. The cases of positive and negative interactions are also discussed.