In reply to JohnV:
The Wilderness Medicine Society recommends that once above 3000m, you should stick to a maximum ascent of 500m per day, with a rest day (no ascent) every 3-4 days or 1000m.
You can climb higher each day (including the rest day) but should sleep no higher than this.
This is "safe" for most people - some people will still get AMS, especially if other factors are involved (stomach bugs, colds, strenuous activity, etc.)
https://www.ncbi.nlm.nih.gov/pubmed/20591379
What trekking companies actually do is not necessarily in line with this, for example a 5-day ascent of the Coca-Cola route on Kilimanjaro is much faster (and causes very high rates of serious altitude-related illness).
0m - 2700m - 3300m would probably be an acceptable ascent profile. Altitude can be unpredictable and still cause problems on "safe" ascent profiles, so a bit of common sense is still necessary.
Post edited at 01:06