The antonyms for the phrase "more woolgathering" would be "alert", "focused", "mindful", "attentive", "vigilant", and "aware". These words describe a state of high level of cognitive awareness and presence. When someone is alert and focused, they are less likely to engage in woolgathering or daydreaming. Their mind is sharp and clear, and they are able to pay attention to what is happening around them. Being mindful and attentive allows one to fully engage with their surroundings and be present in the moment. Vigilance and awareness are crucial in situations where one needs to be alert and cautious. By being vigilant and aware, one can prevent accidents or mishaps from occurring.