We study the online graph coloring problem restricted to the intersection graphs of intervals withlengths in[1,σ]. Forσ= 1it is the class of unit interval graphs, and forσ=∞the class of allinterval graphs. Our focus is on intermediary classes. We present a(1 +σ)-competitive algorithm,which beats the state of the art for1< σ <2, and proves that the problem we study can be strictlyeasier than online coloring of general interval graphs. On the lower bound side, we prove that noalgorithm is better than5/3-competitive for anyσ >1, nor better than7/4-competitive for anyσ >2, and that no algorithm beats the5/2asymptotic competitive ratio for all, arbitrarily large,values ofσ. That last result shows that the problem we study can be strictly harder than unitinterval coloring. Our main technical contribution is a recursive composition of strategies, whichseems essential to prove any lower bound higher than2.