<p>The Horowitz-Hubeny method has been used to compute the quasinormal frequencies of asymptotically anti-de Sitter backgrounds. For the dimensionally reduced BTZ black hole, in this work we propose a modification of this method and we also use a new procedure to calculate its quasinormal frequencies in a perturbative way. The proposed modification of the Horowitz-Hubeny method works for parameter values of the dimensionally reduced BTZ black hole for which the original version of the method does not converge. The proposed calculation of the quasinormal frequencies in a perturbative series takes as a basis a recently published perturbative method motivated in the improved asymptotic iteration method, and in the dimensionally reduced BTZ black hole, for small values of the inner radius, the perturbative values of the quasinormal frequencies coincide with the numerical values. Furthermore we explore numerically and analytically the quasinormal frequencies of the dimensionally reduced BTZ black hole in the near extremal limit.</p>