Combination of p-values from multiple independent tests has been widely studied since 1930's. To find the optimal combination methods, various combiners such as Fisher's method, inverse normal transformation, maximal p-value, minimal p-value, etc. have been compared by different criteria. In this work, we focus on the criterion of Bahadur efficiency, and compare various methods under the TFisher. As a recently developed general family of combiners, TFisher cover Fisher's method, the rank truncated product method (RTP), the truncation product method (TPM, or the hard-thresholding method), soft-thresholding method, minimal p-value method, etc. Through the Bahadur asymptotics, we better understand the relative performance of these methods. In particular, through calculating the Bahadur exact slopes for the problem of detecting sparse signals, we reveal the relative advantages of truncation versus non-truncation, hard-thresholding versus soft-thresholding. As a result, the soft thresholding method is shown superior when signal strength is relatively weak and the ratio between the sample size of each p-value and the number of combining p-values is small.