This paper concerns the RSA system with private CRT-exponents. Since Chinese remainder representation provides efficiency in computation, such system is of some practical significance. In this paper, an existing attack to small private CRT-exponents is analyzed. It is indicated that this attack makes nice use of lattice in RSA analysis, but some argument does not hold in general. Several counterexamples are constructed. Refinements and more precise statements of the attack are given. This paper concerns the RSA system with private CRT-exponents. Since Chinese remainder representation provides efficiency in computation, such system is of some practical significance. In this paper, an existing attack to small private CRT-exponents is analyzed. It is indicated that this attack makes nice use of lattice in RSA analysis, but some argument does not hold in general. Several counterexamples are constructed. Refinements and more precise statements of the attack are given.