complementary goods paradox

Assume that CD players and CDs are complementary goods. Say the demand for CD players decreases because competing products become more popular. As a result, the demand curve for CD players shifts left and the price of CD players falls, but so does the equilibrium quantity of CD players sold. If CD players and CDs are complements with negative cross price elasticity, then the fall in the price of CD players should increase the demand for CDs. But the demand for CD players has in fact decreased. So wouldn't that also tend to decrease the demand for CDs?

In general, when considering the impact on the demand for good B, does it matter if the price reduction in complementary good A is caused by a rightward shift in the supply curve for A or a leftward shift in the demand curve for A?