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Some simple lower bounds for the probability of error for band-restricted digital communication are presented. The bounds revolve two values of the complementary error function, the system SNR, the peak value, second moment, and sometimes, the fourth moment of the intersymbol interference. Contrary to other available lower bounds, no parameter searches or infinite series computations are required. The bounds hold when the system "eye" is open and in some cases when the source symbols are correlated.