A jerky shift is caused by mismatching the engine rpm to the rpm of the gearbox, especially when you let out the clutch rapidly. The cure is to match the engine and transmission rpm for the upcoming gear and/or let the clutch out slowly. Of course, the worse the mismatch the more clutch wear you produce when trying to smooth out the shift by gradually (slowly) engaging the clutch, so rpm matching is the goal. From a stand-still start you have no choice. But otherwise, the more skilled the driver, the more able he/she is able to make a smooth shift by letting the clutch out when the rpm of the engine closely matches the rpm of the transmission.
My wife is a "fast shifter" which is to say, when going from one gear to the other she slams the shifter into the next gear and lets the clutch out quickly, just one step shy of what we used to call "speed shifting" back in the day. The only difference is she at least lets off on the throttle for a moment. She has never rebuilt a transmission but I have and since I have seen syncronizers up close and personal, I shift more slowly in my daily driving. I like to push the shifter toward the next gear and more or less let it ease into the next position kind of "finding it's own way" rather than just forcing it like my wife does. My technique isn't really slow per-se, but it is not as brutal as the way my wife does it.
Those of us who have been married for nearly 50 years as I have know all about balancing the cost of a clutch replacement against the cost of a divorce. Clutches are cheaper, so I just keep my mouth shut when I'm her passenger.
Of course, letting off the throttle while shifting (like we almost always do) causes the rpm to drop which is what you want on an upshift. My wife's technique of quick shifting works out OK because she's in the next gear with the clutch out almost as quickly as a PDK. But for just cruising around town, my less-insane shifts let the rpm drop too much so I compensate with a quick throttle blip as I try to match engine rpm, transmission rpm, and the precise timing of letting out the clutch. As I write this, it sounds complicated but it's really simple and works well with a little practice and a certain amount of sympathy for your syncronizers.
Of course, a more aggressive throttle blip is called for on down shifts where you need the engine rpm to increase in order to match the next lower gear unless you shift like my wife who just jams it into the next lower gear and pops the clutch, syncronizers be damned.
I want to be clear that I don't actually try to modulate the throttle in such a way that I hold the engine at the perfect rpm during a shift. In theory, that is possible, but in practice WAY too difficult. I just blip the throttle with the clutch disengaged causing the rpm to rise quickly to a point above the "perfect" rpm and then as the revs drop back down I try to catch it at just the right point in time. The peak rpm when you blip the throttle will be higher on downshifts than on upshifts. As the rpm falls I try to coordinate the timing and rate of clutch engagement to product a nice smooth transition from one gear ratio to the next. Again, I'm making this sound really complicated, but it is quite simple and with a little practice it becomes second nature for those times when you're just cruising around town taking it easy.
Naturally, when maximum acceleration is called for, my upshifts are much more aggressive without any throttle blipping; i.e. I drive like my wife.
But even when driving aggressively, I blip the throttle on downshifts to produce smooth shifts and save wear and tear on both the clutch and syncronizers.
Bottom line: The better you match the engine rpm and transmission rpm the more quickly you can let out the clutch in order to produce a smooth shift and enjoy the benefits of reduced clutch wear.
