Combination adjustable diameter drinking vessel sleeve and recyclable beverage coaster

An apparatus, comprising:

• a larger diameter drinking vessel;
• and a sleeve side wall sheet having a first side wall sheet end and a second side wall sheet end and being coiled into a tubular sleeve configuration having a sleeve circumference, said first side wall sheet end being radially spaced inwardly from said second side wall sheet end, and comprising an adjustment lever structure pivotally interconnecting said first and second side wall sheet ends and extending radially inwardly from said first side wall sheet end to define a lever tab portion;
• said lever tab portion being pivoted toward said first side wall sheet end to circumferentially space said first side wall sheet end and said second side wall sheet end apart from each other such that said sleeve is in a larger diameter mode, said sleeve encircling said larger diameter drinking vessel, said larger diameter drinking vessel bearing against said lever tab portion and thereby obstructing said lever tab portion against pivoting.

An apparatus, comprising:

• a smaller diameter drinking vessel;
• and a sleeve side wall sheet having a first side wall sheet end and a second side wall sheet end and being coiled into a tubular sleeve configuration having a sleeve circumference, said first side wall sheet end being radially spaced inwardly from said second side wall sheet end, and comprising an adjustment lever structure pivotally interconnecting said first and second side wall sheet ends and extending radially inwardly from said first side wall sheet end to define a lever tab portion;
• said lever tab portion being pivoted toward said second side wall sheet end such that said second side wall end overlaps said first side wall end such that said sleeve is in a smaller diameter mode, said sleeve encircling said smaller diameter drinking vessel, said smaller diameter drinking vessel bearing against said lever tab portion and thereby obstructing said lever tab portion against pivoting, thereby retaining said sleeve in the smaller diameter mode.