The antonyms for the word "most mishandled" can be "well-handled", "carefully-managed" or "efficiently-operated". When something is well-handled, it means it has been managed properly with great care, attention and skill. Carefully-managed represents the act of handling something with caution and prudence, ensuring that everything is done with meticulousness. Lastly, efficiently-operated denotes that a particular task or responsibility has been carried out with the best use of time, resources and energy without any wastage. By using these antonyms, it becomes evident that the opposite of mishandling something is to handle it with competency, dexterity and proficiency, leading to the desired outcome.