I start every exercise with 3 sets of 3 reps, then I add between 1 and 3 reps each workout, so that it takes me very long to achieve 3 sets of 15 reps. Then I increase the load and start again with 3 reps.
The rationale behind this is maximizing safety, avoiding tendinitis and other possible injuries. After I spent more than a year recovering from a painful shoulder surgery, I decided I would do my best to avoid a similar situation in the future.
The thing is, I am not sure if I am wasting my time, of if the high rep range is at all safer. I get sometimes pretty sore even when I am close to the high-rep range of each cycle.
The goal is strength, but I cannot work always in the low rep range because I am 42 yr and prone to overuse injuries. I must somehow cycle between low and higher reps, but, isn't it going up to 15 reps too much?
From Dave's answer I understand that it might be a good idea to implement some short of microcycles, so that I alternate more often between the strength and endurance ends of the rep spectrum. I have posted a new question on how to implement that specifically in my case. But I still hope for other possible approches here (e.g., leaving the cycle from 3 to 15 reps as it is now but reducing the number of sets close to the high end?)