We tend to try to do any vaguely longer term/important estimation as a team exercise, which ends up with people talking each other's estimates up, not down - yo

We tend to try to do any vaguely longer term/important estimation as a team exercise, which ends up with people talking each other's estimates up, not down - you explore the problem space more effectively as a team and a lot of "but what about X" stuff comes out of the woodwork then. If you have a manager who sets your team up for pressure and failure by artificially revising your estimates down, without cutting the scope of the work, then personally, I would find a new manager. Source: Am a manager.