Method: Subjects with bilateral upper extremity essential tremor, on no essential tremor therapy, or on a stable-dose therapy, will have laboratory tests and EKG tests at a screening visit. Eligible subjects will have baseline tremor assessments with standardized rating scales. The tremor will be videotaped. In the first titration step, all subjects will take memantine at the dose of 5 mg/day for 2 weeks, then 5 mg twice a day for another 2 weeks, and tremor again assessed. In the second titration step the dose will similarly be raised to 20 mg/day, taken as 10 mg twice a day, and tremor assessed 4 weeks after the last tremor assessment. In the third titration step, the dose will be raised to 30 mg/day, taken as 15 mg twice a day, and tremor assessed at the conclusion of the third titration step. In the fourth titration step, the dose will be raised to 40 mg/day, taken as 20 mg twice a day, and tremor assessed at the conclusion of the fourth titration step. The dose will be adjusted downwards if titration is not tolerated. Subjects who achieve a clinically meaningful tremor reduction will enter a 12-week extension study assessing the stability of the tremor response.