If you're lucky enough to own a monitor with direct hardware calibration (basically, any NEC PA Series monitor, Eizo ColorEdge monitor, or BenQ PG monitor), then you've enjoyed the benefits of easy and high quality direct hardware calibration.
One thing not often mentioned with respect to this is the need to calibrate these monitors multiple times in a row for the very best results - especially with a new monitor, or with a monitor that has not been calibrated for an extended period. If you calibrate on a tight schedule, say every couple of weeks, this is not necessary, but if you only calibrate now and again, it's well worth running through the process multiple times in a row.
Calibrate multiple times with direct hardware calibration, for a more accurate result!
The reason this gives the best results is that the hardware calibration systems spend a limited amount of time in the actual calibration stage of the process when they're measuring and making physical adjustments to the monitor's display. Because they want the software to execute in a reasonable time, only a limited amount of tweaking is done in any one calibration session. Sometimes there are options in the preferences to increase the time this stage takes, it depends on the system and the calibrator you're using.
The easy way to ensure that it spends plenty of time tweaking your monitor is to simply run through the whole process twice, or indeed even 3 or 4 times. This will often result in significantly better calibrations and lower deltaE numbers in the validation stage. Given the whole thing is essentially automatic, it's well worth the trouble of triggering it twice when you do sit down to do it.