The SPEC system (Speech Predictive Encoding Communication), is a bandwidth reduction method, which employs digital speech interpolation techniques. The differences between the estimated and present values of the samples of speech signals are compared, in a Processor, with a threshold which can be fixed or derived from a table. The estimated value used in the comparison is the one of the previous instant, which can be considered as a zero-order prediction. The main purpose of this work is the investigation of the effect of the use of higher order predictors to estimate samples in the SPEC system. At the same time, the system performance with a Processor where the differences between the estimated and the present values of the samples are ordered according to their magnitude is investigated. With this Processor, the samples corresponding to the greater non-compressed differences are transmitted, which contributes to minimize the system overload noise.