A method for constructing asymmetric space-time block codes (ASTBC) is proposed. This Smart Puncturing Method (SPM) generalizes the so-called subfleld construction method (SCM) introduced in earlier work and applies to any antenna combination with #Rx<#Tx as opposed to SCM, where the requirement is #Tx= m#Rx for some integer m. It has been shown that e.g. for 4Tx+2Rx antennas, the SCM performs equally or even better than the trivial puncturing method (TPM), but admits at the same time lower peak-to-mean power ratio. This is due to the fact that there are no zero slots in the code matrix but the information symbols are evenly spread into the matrix slots. The generalized method proposed in this paper is also based on cyclic division algebras (CDAs) and allows us to do the same for any number of receiving antennas #Rx<#Tx.