Can I go from a 38DDD to a 38C? How much breast can safely be reduced in a breast reduction?

A physical exam coupled with your surgeon's experience will best answer your question.  Cup sizes are not the best measure of the final size.  The breast should be proportionate to your frame.

The amount of breast tissue removed during a breast reduction is based on two things - the patient's own goals and the safety of removing that amount of tissue.  On examination, a surgeon should be able to measure you and give you an estimate of how much should be removed, and where that may place you cup size afterwards.  No one can tell you exactly what size you will be afterards since there is no standard of measurement.  The goal is to make a person look proportional, while achieveing their size goals and doing that all in a safe manner.  I hope this helps.

Congratulations on your decision to proceed with breast reduction surgery; this operation tends to be one of the most patient pleasing operations we perform. Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. Most patients wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso.
With the goal of improving communication with my patients I find the use of photographs of “goal” pictures (and breasts that are too big or too small) very helpful. I have found that the use of words such as “natural” or “C cup” means different things to different people and therefore prove unhelpful. Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup size may also be inaccurate.
It is possible to reduce the breasts size very significantly. The concern with the amount of tissue removed is related to blood flow to the remaining tissue; if too much tissue is removed in one operation the blood flow to the remaining tissue (including nipple/areola) may be compromised. Part of the tissue that is left in place is called the “pedicle"; this segment of tissue is responsible for delivering the blood supply to the nipple/areola tissue. If the pedicle is made too small (in the effort to reduce the breasts as much as possible) then patient will likely have problems with tissue survival.
The other concern with overly aggressive breast reduction surgery is patient dissatisfaction afterwards. It is not unusual for patients who have lived with very large breasts to want to have as much as possible removed. Care must be taken to be judicious in this removal to avoid an outcome where the breasts are too small in relation (proportionately) to the patient's other body parts.   
I hope this, and the attached link, helps.