Delayed luminescence involving charge-carrier trapping and detrapping has recently been identified as a widespread and possibly universal phenomenon in colloidal quantum dots. Its near-power-law decay suggests a relationship with blinking. Here, using colloidal CuInS2 and CdSe quantum dots as model systems, we show that short (nanosecond) excitation pulses yield less delayed luminescence intensity and faster delayed luminescence decay than observed with long (millisecond) square-wave excitation pulses. Increasing the excitation power also affects the delayed luminescence intensity, but the delayed luminescence decay kinetics appear much less sensitive to excitation power than to excitation pulse width. An idealized four-state kinetic model reproduces the major experimental trends and highlights the very slow approach to steady state during photoexcitation, stemming from extremely slow detrapping of the metastable charge-separated state responsible for delayed luminescence. The impacts of these findings on proposed relationships between delayed luminescence and blinking are discussed.