We have investigated the decoherence of quantum states in two Al/AlOx/Al Cooper-pair boxes coupled to lumped element superconducting inductor-capacitor resonators. At 25 mK, the first qubit had an energy relaxation time T-1 that varied from 30 mu s to 200 mu s between 4 and 8 GHz and displayed an inverse correlation between T-1 and the coupling to the microwave drive line. The Ramsey fringe decay times T*(2) were in the [200-500] ns range while the spin echo envelope decay times T-echo varied from 2.4-3.3 mu s, consistent with 1/f charge noise with a high frequency cutoff of 0.2 MHz. A second Cooper-pair box qubit with similar parameters showed T-1 = 4 - 30 mu s between 4 and 7.3 GHz, and that the T1 and the coupling were again inversely correlated. Although the lifetime of the second device was shorter than that of the first device, the dependence on coupling in both devices suggests that further reduction in coupling should lead to improved qubit performance. (C) 2013 AIP Publishing LLC.