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This paper presents an improved upper bound on the performance of convolutionally coded systems over quasi-static fading channels (QSFC). The bound uses a combination of a classical union bound when the fading channel is in a high signal-to-noise ratio (SNR) state together with a new upper bound for the low SNR state. This new bounding approach is applied to both BPSK convolutional and turbo codes, as well as serially concatenated BPSK convolutional/turbo and space-time block codes. The new analytical technique produces bounds which are usually about 1 dB tighter than existing bounds. Finally, based on the proposed bound, we introduce an improved design criterion for convolutionally coded systems in slow flat fading channels. Simulation results are included to confirm the improved ability of the proposed criterion to search for convolutional codes with good performance over a QSFC.