A memory controller circuit arrangement and method utilize a tuning circuit that dynamically controls the timing of memory control operations, rather than simply relying on fixed timing parameters that are either hardwired or initialized upon startup of a memory controller. Dynamic control over the timing of memory control operations typically incorporates memory test control logic that verifies whether or not a memory storage device will reliably operate using the dynamically-selected values of given timing parameters. Then, based upon the results of such testing, such dynamically-selected values are selectively updated and retested until optimum values are found. The dynamically-selected values may be used to set one or more programmable registers, each of which may in turn be used to control the operation of a programmable delay counter that enables a state transition in a state machine logic circuit to initiate performance of a memory control operation by the logic circuit. Dynamic tuning may also utilize a unique binary search engine circuit arrangement that updates one of two registers with an average of the current values stored in such registers based upon the result of a test performed using that average value. By selectively updating such registers, a fast convergence to an optimum value occurs with minimal circuitry.