This paper considers the detection of fluctuating targets via dynamic-programming-based track-before-detect (DP-TBD) in radar systems. Swerling targets of types 0, 1, and 3 are considered. DP-TBD usually integrates either squared amplitude or the logarithm of the envelope likelihood ratio (LELR) scoring functions. Thus, only amplitude information is taken into account regardless of the fact that the measurements are often complex valued. In this paper, the phase information is used in the integration process of DP-TBD to enhance radar detection performance. More precisely, the logarithm of the complex-measurement-based likelihood ratio (LCLR) is used, taking the place of squared amplitude or the LELR. First, we derive the expressions for the LELR and the LCLR for the three Swerling types. Then, to reduce the complexity of computing LELR and LCLR, we also propose efficient but accurate approximations for the LELR and the LCLR. Simulations are used to assess the performance of different DP-TBD strategies.