Due to geologic and tectonic events many reservoirs have an elongated geometry in which dual-linear and single-linear flow regimes may be developed. The single-linear flow may be altered by changes in facies (mobility) or reservoir width (composite reservoir). Therefore, it is desirable to identify and characterize these types of systems which lead to competent decisions and adequate reservoir management. The identification and determination of parameters for such reservoirs are conducted by conventional techniques (straight-line method), type-curve matching of pressure versus time and the Tiab’s Direct Synthesis (TDS) technique. This last one has been lately presented for homogeneous and constant width reservoirs. In this paper, an extension of the TDS technique to incorporate variations in either mobility or reservoir width is presented. Several simulation experiments were run to understand the behavior of the reservoir under these new conditions. If the change of the mentioned parameters takes place after the dual- linear flow has ended a new half-slope line is observed on the pressure derivative curve. This new line is shifted upwards the original dual-linear line without regarding the variation of one of the studied parameter. When, the anomaly occurs during dual- linear flow the new half-slope line of the pressure derivative curve may be shifted upwards or downwards depending upon the magnitude of either mobility or reservoir width. This new line may not be referred as linear flow regime because it is really not. We have named it as pseudo-linear flow regime, instead. Therefore, a modification of the intercept of the ½-slope line from 0,5 for dual-linear flow regime to a greater or smaller value, which may be different from (single-linear flow case) has to be considered in order to provide new equations for the estimation of new values of either permeability or reservoir width. The proposed methodology was successfully verified by interpreting both synthetic and field pressure tests for elongated oil reservoirs which involve changes in either mobility or reservoir width during the path of the transient wave.