A cost function, utilizing the signal amplitude as well as the phase information, yields fast convergence and small mean square errors, when used for equalizing dynamic wireless channels. Recently, it has been shown that the minimization of cost functions that include both amplitude-dependent and constellation-dependent terms leads to improved receiver performance for high-order signal constellations, compared to that achieved by only using either term. The amplitude-dependent term corresponds to the constant modulus algorithm (CMA), which ensures proper global convergence properties. On the other hand, the constellation-matched error (CME) term provides desirable local convergence properties. Two possible schemes can be used for presenting a combined cost function. One scheme is based on a weighted sum of the CMA and the CME terms, where the weights are fixed, whereas the cost function in the other scheme has time-varying weights that are recursively update using gradient techniques. In this paper, performance comparison is conducted between techniques implementing combined cost functions with fixed and variable weighting parameters. The comparison also includes the CMA and DD techniques as well as adaptive equalizations based on dual modes. In the latter, one term of the cost function is considered at one time. The common dual-mode approach calls for initialization with CMA and thereafter switching to a proper constellation-matched algorithm.