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Regarding familial tremors, research is sparse concerning essential or familial tremors and diet. One study showed that cutting back on red meat consumption may help reduce the occurrence and progression (this was mainly for men, however may be something to consider).
Research on omega-3s is underway and may be worth trying as these healthy fats provide a wealth of nutritional benefits.
A Mediterranean-style diet would fit these recommendations.
Another finding is that weight training, or weight-bearing activities, improves steadiness and decreases the magnitude of tremors. Behavioral relaxation training was also found to reduce tremor severity.