I concur that applying to the second round is still a good idea. However, note that some schools encourage students to apply as early as possible.
"When should I apply for admission?
A: Given the competitive applicant pool, you are encouraged to apply as early in the admission cycle as possible. Candidates whose ability to enroll is dependent upon receiving merit-based aid should apply during round 1 or 2. Candidates who applied the previous year are strongly encouraged to reapply for admission during round 1."
"Should I apply for Round 1?
Applicants are encouraged to apply in the earliest round possible. Although there is no particular preference given to applications submitted in Round 1, applications are reviewed in the order received, and it is possible that many of the offers of admission will be made from Rounds 1 and 2."