Time decay for solutions to the initial-value problem for the linearized Vlasov equationis studied. HereEx= ρ= ∫gdvandf(v2) ≥ 0 is to be sufficiently smooth and strictly decreasing. The initial value forgis to be suitably smooth and small at infinity. Whenf1(v2) → 0 as |v| → ∞ at an algebraic rate, it is shown that ρ → 0 at an algebraic rate ast→ ∞ in both theL2and maximum norms. Whenfis a Gaussian, the decay rate is logarithmic. The fieldEis also shown to decay in the maximum norm for both generic classes off's. Similar results are obtained in three dimensions for spherically symmetric data. Whenfhas compact support, no decay of the density inL2(R1) is possible for data of compact support.