Optimal delivery of chemotherapy intensity is dependent on host- and tumor-specific characteristics. In this article, the chemotherapy late intensity schedule is revised to account for tumor growth instability, where a small tumor cell fraction emerges that exhibits a higher proliferation rate than the parent strain. Modeling this instability as simplified two-population dynamics, we find that: (a) if this instability precedes the onset of treatment, the slope of the linear increase of the drug concentration for the standard "Norton-Simon late intensity schedule" changes and the initial value of the dose strongly depends on the ratio of the two tumor cell populations and on their distinct growth rates; and (b) if the instability trails the initial treatment, the effective chemotherapeutic drug concentration changes as well. Both cases point toward testable potential refinements of the Norton-Simon late intensity schedule.