The alternating least squares (ALS) method is frequently used for the computation of the canonical polyadic decomposition (CPD) of tensors. It generally gives accurate solutions, but demands much time. A strong alternative to this is the alternating slice-wise diagonalization (ASD) method. It limits its targets only to third-order tensors, and in exchange for this restriction, it fully utilizes a compression technique based on matrix singular value decomposition and consequently achieves high efficiency. In this paper, we propose a new simple algorithm, Reduced ALS, which lies somewhere between ALS and ASD; it employs a similar compression procedure to ASD, but applies it more directly to ALS. Numerical experiments show that Reduced ALS runs as fast as ASD, avoiding instability ASD sometimes exhibits.