Denote by w _n* and w_n the exponents of Diophantine approximation defined in Mahler’s and Koksma’s classifications of transcendental numbers, respectively. We prove that there are p-adic T-numbers x such that w_n(x ) − w_n*(x ) is any number chosen in the segment [0, (n −1)/n] for all positive integers n and for w_n(x ) large enough. Thus we improve Schlickewei’s result that p-adic T-numbers do exist.