Sequential sampling plans are appealing because fewer observations are needed than those needed for fixed sampling plans to make a terminating decision when insect populations are sparse or abundant. Wald's Sequential Probability Ratio Test (SPRT) commonly has been used in monitoring insect populations and damages from these populations. At times, particularly for moderate infestations, the SPRT with its parallel boundaries takes longer than a comparable fixed-sample-size method to make a terminating decision. An alternative sequential testing procedure called the 2-SPRT for the negative-binomial parameter P is demonstrated. The value of the exponent k is assumed to be known. In this procedure two one-sided SPRTs are performed simultaneously, which results in the convergent boundary lines. The average number of observations needed for the terminating decision for medium infestations (i.e., for P1