I've experienced working at very structured companies which things move really fast and projects are closed well (lots of MBAs, VPs and project managers), that company was not a tech company, but I've noticed that the output of the work in terms of quality and innovation really sucked. People had a "factory worker" mindset, just keep doing the same stuff even if things were failing until someone at the upper management decided a different thing. I came back to a company that I worked a few years ago which I love, that has lots of engineers and makers (designers, tech support with technology background). They create a lot of amazing things, but things move very slowly and we are not growing fast enough. I've watched this: https://vimeo.com/34081566 and I was really surprised by Mailchimp's culture. How can slow company move faster without hiring stupid people that just put pressure and make people's lives miserable? Can a company move faster using more analytics? Note: it's not Saas but hardware and offline software.
It IS about hiring. And that comes from the attitude of the leadership. If you have lazy workers, have a look at the hiring leaders.
You can easily adapt methodologies like SCRUM or SREDIM to your situation: http://en.wikipedia.org/wiki/Scrum_%28software_development%29
Instead of project manager, the team members can assign roles--advocacy roles--to themselves.
I think ideally you would want smaller teams with bigger responsibilities, and accountability. You want them focused on the projects that provide the highest return.
The trick is to hire attitude and train for desired skills. Many places seem to do it backwards. They want a specific skill and forget that humans perform the work.
Teams will figure out their own dynamics and make things work. But you need to ensure that there is enough cross team interactions to ensure everybody is pulling in the same direction.
Also make sure the space is conducive to information exchange. At Tech Group, we used completely open spaces. No walls. So anybody could simply raise their head and communicate with anybody else. Conference room used for collaborative in-team tasks.
A company like that might turn some of the design thinking of the makers and engineers against it's own process issues and ask the creative culture to creatively and collaboratively solve it's own issues. I've had clients hold periodic closed-door meetings where staff teams had to solve internal problems and present their solutions to other staff teams for a "vote" on what gets implemented. Essentially they run their own innovation lab but the target isn't on product, but on process and matching new processes to internal needs that, when done correctly, achieve buy-in.
software IS 99% about people. One thing, u have to define "fast enough". Amazing things are not done in one friday afternoon. Polishing, licking if u want, takes time. A lot. And, analytics has nothing to do with it. For fast projects, u may need different kind of people, who can cut corners and sacrifice some qualities and thoroughness for speed. But u still need pressure to cook something. A project always soaks all the time u give it. Hence the kind of people who can push. Few can both push/lead and dev/design. Find some. On another note, u may have something completely broken in the management, company values and their perception, and all that. Culture is not just a single definition/motto/slogan. It takes gumption.
This is an ongoing challenge in creative environments. Having the right people in the right positions is critical. It's also helpful to empower functional experts to take the reins when its time to show the creative products. Functional experts can save time and money if they're included in the project planning phase and if they're allowed to represent themselves and their work to the client. The PM can then keep a watchful eye on costs, time management and client satisfaction. And, your functional experts will be happier, satisfied and more understating when it comes to finishing a project on time.
My initial thoughts are that if you have clear goals for your teams, they will perform according to those measures you set. Consider what processes you are using as well? To maintain creativity you still need to have a process that encourages completion. A third idea is to have at least one or two facilitators in your team that are responsible for assuring you are meeting the goals and expectations for the team. It could be a team leader or it can be a role that changes from project to project and that all members of the team have skills in facilitating the team's approach.
Unfortunately, you can't. You need project managers. The key is hiring the right ones :)