There seems to be some misconception as to how a 5C collet functions. Firstly, the grip range of all my collets are about 1.2" long. Secondly, to function properly, a 5C collet grips the work along its entire length of the cylindrical bore.
The drawing below shows a 5C collet in a collet chuck. The collet' features include a cylindrical work holding region, A, formed by three split fingers and a flexure region, B. When a work piece that is smaller than the nominal diameter is inserted and the collet tightened, the collet fingers will bend in region A to grip the work. The collet first bends in a simple arc at point F, shown exaggerated for purposes of illustration, causing the collet fingers to grip the work at C, and pulling the fingers away from contact with the chuck at E with point D providing the contact with the chuck.
At this point, the clamping of the work is unstable as it is only a ring of contact and the work can pivot around that point. This can easily be demonstrated by mounting an undersized bar in a collet, using only enough clamping force to grip the work. If you apply force to the far end of the bar, the bar will deflect and will take a new position, as can be verified with a dial indicator.
Further tightening draws the collet deeper into the chuck, forcing the collet flexure region to take a "S" shaped curve with bends at F and G until the collet makes contact with the work along the entire surface A and point B is again in contact with the chuck.
It is often recommended that undersized work should be limited to .003" less than the nominal diameter. This is because forming the "S" curve introduces considerable stress to the collet fingers which increases dramatically as the work diameter departs further from the nominal diameter. There is another reason as well and that is when the work diameter is less than the nominal diameter of the collet, the collet fingers only make contact with the work along three lines, shown as points F in the end view. This is why "emergency" collets are used when the number of pieces justifies the additional machining. The collet is bored to exactly match the work, insuring contact around with the full work surface.
A 5C collets ability to grip undersized work is limited by the width of the slits between the fingers and by the ability to tighten the collet in the chuck. The smallest diameter that can be gripped by a 5C collet is slightly less than the nominal diameter less the slit width, in theory. In practice, the force required to properly close the collet on the diameter may be more than can be applied by the collet closure mechanism. The slits on my collets are between 019" for the 1/16" collet and .055" for the larger collets. A collet set by 1/16th's would not be able to cover all possible diameters. A set by 32nd's would be able to close on any diameter within its range. A set by 64th's would create less stress on the collets in the case where the work diameter was slightly oversize for a nominal collet, requiring to go to the next larger size but may not be warranted for the occasional user.
For the user not wanting to purchase a set by 32nd's, there is a suitable workaround. A shim made from a beverage can will increase the diameter of a piece of stock by about .008" and some roofing flashing by .020". Cut a length slightly less than the circumference of the work and roll around the work. Insert the work and position the end of the shim next to one of the collet slits. Tighten and you're good to go.
Edit: deleted redundant drawing.