We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems with pointwise time-varying input delays. Our method circumvents the problem of constructing and estimating distributed terms in the stabilizing control laws, allows arbitrarily large input delay bounds, and covers dynamics with uncertainties. Instead of using distributed terms, our approach to handling longer delays is to increase the number of predictors, and we obtain explicit formulas for lower bounds for the number of required predictors. The lower bounds are functions of the bounds on the delays and their derivatives. We illustrate our method using a pendulum dynamics.