The ion tearing instability is investigated in a magnetotail configuration that consists of a diffuse plasma sheet current and an embedded, thin current sheet with a strong current. For historical reasons, the thin embedded current sheet will be called a "neutral sheet", even though the normal component of the magnetic field, B(n), is nonzero. In particular, we assume that the current within the thin current sheet is due to the acceleration of "Speiserlike' ion trajectories by a cross-tail electric field E(y). It is found that the strong current within the neutral sheet is essentially unimportant to the growth rate of the tearing instability, and that the growth rate scales as (lambda0/L(z))2, where L(z) is the overall half thickness of the plasma sheet, lambda0 is the ion inertial length, c/omega(pi), and omega(pi) is the ion plasma frequency at the neutral sheet edge. In the absence of the current outside the neutral sheet, current filamentation is stable.