We consider the scheduling model with two identical machines and jobs which arrive online in a list and are assigned to the machines with the objective of minimizing the makespan. Differently from the pure online version, we know in advance a lower bound and also an upper bound on the total size of all jobs. Our algorithm improves previous results on some interval of r, where r is the ratio of the upper and lower bounds on the total size. For most ranges of r our algorithm is best possible. Our technique is based on a smart application of so-called “safe sets”.