A comparison is made between two classes of Vlasov equilibria with respect to the ion tearing mode instability. The first class is that of a current sheet in equilibrium with a vacuum (Harris type). The second class is that of a current sheet in equilibrium with a magnetized background plasma. The comparison is made via a simple magnetoinductive simulation involving ions alone. We find that the presence of the background species has several dramatic effects. The linear growth rates are affected, the tearing mode an be stabilized or destabilized by the background plasma, and the exchange of energy between particles and fields is affected. In particular, the saturation wave energy level of the tearing instability can be either enhanced or reduced by a factor of 10 from the Harris type depending on the depth of the penetration of the bakground particles into the neutral sheet.