Deadlines can be achieved even on a complex project if:
1 estimates are created by people who have experience in the field.
2 estimates are peer-reviewed honestly and thoroughly.
3 estimators are insulated from customer stated timescales.
4 if the total estimate is too big, the deliverables or the resources should be tweaked: never the estimates.
5 each estimator's estimates are tracked against delivery to establish their over/under estimate record.
6 estimator's under/over estimate track record is used to validate their estimates.
7 continued, regular, honest estimates are encouraged as the project progresses.
8 proper project management is applied to tweak features/quality and resources to correct any divergence as soon as it becomes apparent.
9 reward those whose estimates are proved to be accurate.
Points (5) and (6) are important: each person is prone to being optimistic or pessimistic, and both traits need to be corrected within reason before an estimate is adopted.
Points (7) and (8) ensure that estimates are updated and that corrective action is applied. "Head in the sand" isn't a good way to meet deadlines.