There are some health benefits associated with green and black tea ingestion that are thought to be more reflective of the Theanine content rather than the Green Tea Catechins or the Theaflavins, and this is thought to be related to (as L-Theanine positively regulates nitric oxide) cognitive benefits.  Although, L-Theanine primarily promotes relaxation without sleepiniess.  

Interestingly, the relaxing and attention promoting properties of L-Theanine coupled with the lack of sedation tout L-Theanine as L-Theanine's most significant supplemental role in reducing the 'edge' of many stimulants.  Together, L-Theanine and Caffeine are known to be synergistic in creating focused cognitive behavior and attention.

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Benefits

• A combination of L-Theanine with Caffeine is noted to be synergistic in promoting cognition and attention
• Theanine is relaxing, but does not appear to induce sedation (cause sleep)
• Caffeine is a stimulatory anti-sleep compound extracted from coffee beans.
• Caffeine is a powerful stimulant, and it can be used to improve physical strength and endurance. It is classified as a Nootropic because it sensitizes neurons and provides mental stimulation.
• A combination of L-Theanine and Caffeine are known to increase overall mood of an individual.