Fixed Cost and Outcome
To quote from the Agile Manifesto, we value customer collaboration over contract negotiation. A common challenge with fixed cost and fixed outcome engagements is handling change, since requirements do change, and one of the best things about a good demo is engaged stakeholders providing feedback and ideas for improvement.
With a bit of care,engagements on this basis can work well - use of contingencies and allowances, and a bit of give and take on both sides will often provide the best results. One of the hardest aspects to control is quality, since it can be subjective and difficult to measure.
As a client or sponsor, instructing work on this basis can work well for discrete and easily defined tasks such as integrations, infrastructure and adding new features to established and well-maintained existing projects.