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It depends. You can always ask.

Here is how it works for the two major companies: Vinasun and Malinh. The drivers here drive 24 hr shift and rest the next day. They share the car with another driver who drives the next 24 hours, so you have to make arrangement with at least two (either sharing the same car or driving two different cars on alternate days).

It is against the regulation for them to turn the meter off so can't advice you on the fixed rate scheme, but if they drive on the same route, it would statistically even out on the long run, even on the meter-based scheme.

If it is fear of being ripped off, a solution may be for you to get a Vietnamese to write the driving instruction down on a piece of paper and show it to the taxi drivers you flag on the street and learn to say some Vietnamese at the beginning to the trip to them. Once the drivers see that you know your route/have been here sometime, they will be more hesitant to cheat you.

Take a few more rides, find someone who can communicate with you reasonably well and hooked him (or her!) up.  Most taxi drivers are more than willing to be your regular, but of course if your hours are weird then may be tougher.

This is the way I hooked up a Saigon Tourist taxi driver, realised he worked in a group, and had been using them for the past few months - sometimes my flights are delayed and they are still there waiting for me at the airport after a few hours.  Even not, all I need to do is to give a call and one of them will come in 15mins.

However all these conveniences sometimes may come at a price, since you must acknowledge that the driver is giving up his street jobs to serve you.

Eg my ride from airport to Binh Thanh district is at a flat rate of VND165,000.  Compared to the usual metered fare approx VND150,000-VND180,000, I dont have a problem with that at all, I can sleep soundly in the car without having to watch the road, knowing I will never need to go on a 'tour' with a rogue driver again.

Add-on:  None of them turn on the meter, so I guess they do not really care about the regulations.  Lol.  ;P

There are a few privately owned taxi's you could do a fixed contract with.

Pirate taxi's (you can tell them because they have magnetic signs that peel of) and if you find a good one you can do a deal.

Try calling Vina Taxi, they have safe drivers and do corporate contracts which essentially is what your needs are. (Vina are a damn sight safer than Vinasun who are worse than Mai Linh.)