The most efficient approach will be a switching supply, for they convert energy instead of just dropping voltage. In other words, if your regulated load will be drawing 5mW of power (5V*1mA=5mW) a linear supply will draw off of the full voltage of the battery 7V*1mA=7mW. But a switching supply will draw instead 5mW from your battery so the current draw will be 5/7mA of current instead of 1mA. This though is a gross simplification, for in both cases some additional power will be drawn by the regulator circuitry.

Depending on the energy drain curve of your battery you will want either a simple buck switching supply circuit or a boost-buck switching supply. Again, I'll translate my comment to non-geek speak. A buck switching supply is also known as a step down supply. A boost switching supply as one might guess increases voltage. A boost-buck switching supply can do both. Now, if these batteries have a power drain curve of a carbon zinc battery, then a considerable amount of energy is still available when the voltage drops to 80%. If instead these are NiCad batteries then the voltage sags very little before fully exhausting their stored energy. The drawbacks of a boost-buck topology though are the higher total part count and a higher parasitic power loss. Frequently in critical longevity designs, a single battery with a boost switching supply design is crafted to maintain regulation until more than 95% of the battery's stored energy is released.

Now that I've generically answered your question, the most dramatic longevity return is a miserly use of power on the regulated side.

He said that they are 3.6 volts each. That means Lithium-Ion.

He also said his are size RCR14500 AA Protected Cells 3.6v each.

Lithium-ion cells are not available in standard sizes like Alkaline, Nicad and NiMH cells to prevent interchangeing.

Yes, the voltage does imply this being a lithium ion battery. I'm not familiar with that specific package so it might be similar in size to an AA battery, but you are correct that it won't be exactly a AA battery in size to prevent damage to circuits expecting the 1.5V of a AA battery. Despite the length of my initial reply, this ambiguity prevented me from going into more critical details for a lithium ion battery.

Assuming that these are lithium ion batteries, a few added concerns should be included in the discharge power supply circuitry. Lithium ion batteries do have a discharge voltage swing as wide as the old carbon zinc batteries. Since this starts at a higher voltage, this concern is often overlooked. Also to successfully recharge a lithium ion battery, a full discharge to zero volts should be avoided. A carefully crafted switching supply can meet these two requirements. Depending on the quality of regulation the load requires, the two diode suggestion that somebody else posed can also work. It just won't be as efficient as a switching supply.

Right.

There are variations in the dimention info. (that explains why some cells fit too tight.)
Alkaline, NiMH & NiCad Cell Type Dimentions
AA D 13.5–14.5 x L 50-50.5
C D 26-26.2 x L 46-50
D D 33-34 x L 58-61.5

Rechargeable Li-Ion Diameter & Length
18 x 65 mm
18 x 50 mm
17 x 65 mm
17 x 50 mm
14 x 45 mm

Notice the size mis-match.

What losses are there with a couple of rectifiers in series used for level shift at operating current compared to a switcher?

Of course the switcher will use a wider range of input voltage and provide a more stable output complete with all the EMI.

The small switcher (about the size of my thumb) in the automobile charger for my Samsung Renown cell phone puts out 5 volts at 0.7A. Another cell in his battery pack would probably run that in its range.

Relying on just diode drops will provide no regulation. With four diodes, when your batteries drop from 7.2V to 5.2V your electronics will be going from the predicted 4.8V to 3.8V. But that's using the simplest model for a diode. A diode actually has this non-linear equation for it's I/V response i_D=I_oe^[(qv_D/nkT)-1)]. The I_o is the reverse saturation current. i_d and v_d are the diode current and voltage. q is the charge of an electron. k is Boltzmann's constant. n is an empirical scaling constant nominally between 1 and 2. While T is the temperature in Kelvin. So depending on your current draw you will get a different voltage drop per diode.

Lastly, the use of diodes will be a linear drop. So taking the simple model of 0.6V per diode for a 2.4V drop. This will mean while your battery maintains 7.2V, the efficiency of this supply design will be 4.8V*I/(7.2V*I)*100%≈67% [power out/power in]. Certainly a switching supply can do much better and will provide true regulation. There are many out there with thorough application notes. One controller you can find at http://www.onsemi.com/pub_link/Collateral/MC34063A-D.PDF

His batteries don't provide regulation either.

As to regulation, I recall he seems to want no more than a level shift to run a 5 volt device.

It is true that the diodes will contribute to an increase of supply impedence and it would be wise to stiffen it up with a capacitor unless his device has that problem designed in.

The Li-Ion batteries with the graphite negative electrode hold their voltage flat until they are ready to drop at around 80% of capacity and need recharging anyway and the last 20% of capacity is only available for a short time.

Also the diodes would prevent the battery from completely discharging.

Two silicon diodes forward biased should drop the voltage close to 1.2 VDC. That should put you right at 5.0 VDC. Perhaps not the most efficient but cheap and effective. At least it draws no additional current.

Have FUN!
TT3

I appologize for a slight miscalculation. 2x3.6=7.2V not the 6.2 which I came up with through some unexplained mind fog originally. That means that the diode string needs to drop 2.2 VDC if this is to work. Common silicon diodes are usually good for about 0.6 drop so one would need 4 of them to leave the OP with 4.8VDC. This option also limits the discharge to 2.2 VDC if the thing is left on so perhaps it will be less likely to completely discharge the battery.

Have FUN!
TT3

This will step down the voltage, but without any regulation at all.

For a more in depth study on batteries check out http://www.mpoweruk.com/index.htm

Notice the discharge drop curves under performance.