We study vector versions of Halanay's inequality. We provide an input-to-state stability result. Even in the scalar case, we provide tighter bounds than those that were available in the literature. Our key new techniques involve finding componentwise positive vectors in the null spaces of suitable matrices. These matrices are expressible as weighted sums involving the coefficient matrices that occur in the vector versions of Halanay's inequality. We allow time-varying coefficients in our Halanay