We present a flexible hybrid decision scheme for decentralized detection under communication constraints. In this scheme, local sensors send a binary (hard) decision to the fusion center when the local sensors have a relatively high confidence in the decision, otherwise a perfect version of the local likelihood ratio (LLR) is sent. In practice, a finely quantized version of the LLR is sent. The degree of confidence at which this switch is made is determined by the specified communication constraint. The fusion center makes a final decision based on the information received from local sensors. By employing the person-by-person optimization methodology, we develop the local decision rules and the fusion rule. Owing to the associated computational difficulty, we propose a simpler procedure based on the class of Ali-Silvey distance measures to obtain the local decision rules. A numerical example is also presented for illustration.