Deepening -
Once the trance state has been induced it can then be deepened. This usually takes the form of a simple count down from 10 to 1 (along with suitably relaxing suggestions), or perhaps some form of guided imagery, such as descending a long flight of stairs. 
Defence Mechanism -
Usually associated with the 'censor' it is a psychological strategy to prevent painful, repressed or unpleasant material from coming to consciousness, where it might have to be faced and dealt with.
Dehypnotization -
Bringing the hypnotic state to an end and waking the patient. Usually arranged to happen at a particular signal, such as the count from one to five. Always remember to remove or nulify suggestions that you do not intend to remain. 
Demophobia - 
Excessive fear of crowds
Dental Hypnosis -
Typically hypnosis used to minimize the pain of dental surgery or to overcome a patients morbid fear of dentistry.
Depersonalization -
A psychological condition common to many mental illnesses but one which can also be brought about in deep hypnosis when amnesia robs the patient of his immediate personal identity. 
Depression - 
An extended feeling of hopelessness and inadequacy, lowness of mood. Clinical depression (endogenous) is difficult to treat with hypnosis and should only be undertaken with medical supervision. Reactive depression (exogenous depression due to a particular cause, such as losing employment or a loved one) can be treated with hypnosis but great care must still be taken and the patient should be advised to visit his doctor first.
Dermatosis - 
The family of skin diseases. Can have organic and allergic causes but often are due to emotional conflicts and false learnings, in which instance they can respond well to hypnotherapy.
Desensitization -
Desensitization (systematic) is a theraputic method developed in Behaviour Therapy (by Joseph Wolpe) where by the patient is gradually exposed to the source of his anxiety while at the same time engaging in anxiety inhibiting behaviour, such as deep muscle relaxation. Thereby affecting deconditioning.
Hypnosis can be combined to good effect with systematic desensitization to form the therapy of Hypno-desesitization. 
Diagnosis - 
The process of discerning the nature of an ailment.
Direct Suggestion -
An openly stated hypnotic command, direct, authoritative and without guile. It's meaning can be taken at face value. In contrast to indirect suggestion.
Dissociation - 
The seperation of one part of the mind from the other part or parts. Thought to be at the root of many mental illnesses (multiple personalities for example) but is also a phenomenon readily available in hypnosis and active imagination techniques, where it can be used theraputically. Many problems respond to the communication with and 're-integration' of split off parts.
Dominant Effect (The Law of) -
Simply states that a strong emotion will always displace a weaker one (the rule being that only one emotional state can exist in experience at any one time). Try to evoke and connect emotion to your suggestions and they will be much more effective. Also, to move a feeling or emotion out of experience evoke a stronger one. Its difficult to feel anxious when you are angry or happy.