Space-time transmit diversity results in coupling of transmitted symbols across different antennas, which increases the complexity of maximum-likelihood decoding. Symbol coupling can be completely or partially avoided if the space-time code (STC) satisfies specific decoupling conditions; examples of such codes are orthogonal space-time block codes and quasi-orthogonal codes. In this letter, we study decoupling conditions for a linear full-diversity STC. Quasi-decoupled codes are proposed as a partially decoupled full-diversity STC of any rate for any number of transmit antennas with minimum decoding delay. By optimizing the coding gain of quasi-decoupled codes, it is shown that quasi-orthogonal codes have competitive performance with respect to the Alamouti code, and the more-recent threaded algebraic space-time (TAST) codes and ABBA codes. A general full-diversity decoupling condition is considered, and the general solution to this case, which also encompasses previously known orthogonal STCs, is derived