3j symbols: to normalize or not to normalize?

The systematic use of alternative normalization constants for 3j symbols can lead to a more natural expression of quantities, such as vector products and spherical tensor operators. The redefined coupling constants directly equate tensor products to the inner and outer products without any additional square roots. The approach is extended to tesseral harmonics. The methodology developed here leads to a significantly clearer presentation, which is of interest, not only for textbooks but also for researchers using spherical tensors.