Differential-linear cryptanalysis, a combined cryptanalysis method, has been applied to the analysis of many symmetric ciphers. Specifically, for the ARX block cipher SPECK, differential-linear cryptanalysis is an effective technique for evaluating its security. In the latest framework of differential-linear cryptanalysis, the cipher is divided into three components: the differential part, the middle part, and the linear part. These parts contain high-probability differential characteristics, high-correlation differential-linear approximations, and high-correlation linear approximations, respectively. For ARX ciphers, the traditional search process for differential-linear distinguishers typically involves first using experimental methods to obtain a high-correlation differential-linear approximation in the middle part. Subsequently, linear and differential characteristics are searched for forward and backward. However, this strategy may overlook some effective differential-linear distinguishers. This study proposes a search method for differential-linear distinguishers, which integrates the characteristics of the differential and linear parts in high-correlation differential-linear approximations and leverages high-probability differential and linear characteristics. The proposed search algorithm is applied to SPECK, yielding for the first time an 11-round differential-linear distinguisher for SPECK32 and a 12-round differential-linear distinguisher for SPECK48. Both outperform the best-known differential-linear distinguishers for these ciphers.