Integer DCTs have important applications in lossless coding. In this paper, an integer DCT of radix-2 length n is understood to be a nonlinear, (left-)invertible mapping which acts on Z n and approximates the classical discrete cosine transform (DCT) of length n. In image compression, the DCT of type II (DCT-II) is of special interest. In this paper we present a new approach to invertible integer DCT-II and integer DCT-IV. Our method is based on a factorization of the cosine matrices of types II and IV into products of sparse, orthogonal matrices. Up to some permutations, each matrix factor is a block-diagonal matrix with blocks being orthogonal matrices of order 2. Hence one has to construct only integer transforms of length 2. We factorize an orthogonal matrix of order 2 into three lifting matrices and work with lifting steps and rounding-off. This allows the construction of new integer DCT algorithms. We give uniform bounds for the worst case difference between the results of exact DCT and the corresponding integer DCT. Finally, we present some numerical experiments for the integer DCT-II of length 8 and for the 2-dimensional integer DCT-II of size 8 ร 8.