My Fortune colleague Geoff Colvin writes in our March 2 issue that a few companies–DuPont and Colgate-Palmolive and McDonald’s , to name three–are working overtime to preserve their brand equity in this downturn. Instead of discounting, they are, in some cases, actually raising prices.

Another company loathe to cut prices: Starbucks . As I’ve noted on Postcards, CEO Howard Schultz told me last year that the smartest decision he made during this recession was refusing to discount. Investors crying over the stock’s swoon (down 50% this past year) may question his wisdom. But hand it to Howard for floating new ventures–new value-priced breakfast combos, instant coffee, a Gold loyalty card, partnerships with Costco and Bono’s Product RED–in an effort to shore his sales and once-mighty brand.

Given Starbucks’ struggles to preserve its premium image, I have to share with you an amusing story from my neighbor, Lauren Jacobs, who lives next door to me in my Manhattan apartment building.

Lauren is a teacher. She teaches 11th grade in a public school in Spanish Harlem. Last month, she kindly let me borrow her Hewlett-Packard Pavilion PC to set up my new Verizon wireless service in my apartment. I gave Lauren a $40 Starbucks card to thank her.

A lover (read: addict) of coffee and an intermittent Starbucks fan, Lauren decided to have a contest with her dad in New Jersey to see who could spend more money at one time on ONE Starbucks beverage.

Well, he couldn’t even compete.

Lauren’s dad spent about $3 on some sort of cappuccino, neglecting to realize that Starbucks’ cold drinks are the ones that really suck the money out of you. Determined to wallop her dad in this coffee contest, Lauren walked downstairs to our Starbucks. (We live above a Starbucks. We could go in our pajamas, if we were so bold.) Despite the February freeze, she ordered a Venti Mocha Frappuccino with extra whipped cream. It cost $5.75.

Lauren immediately called her father to gloat. She confessed to him that she was terribly self-conscious carrying the drink around the corner and into the building. People in the elevator stared at her as if she were some sort of coffee glutton. “I didn’t know what ‘Venti’ meant,” she lied.

Four hours later, she called her dad back. She was still drinking that Venti Frap. “I felt nauseous and dizzy after I finished–yes, finished the drink. And I did not sleep well that night,” she recalls. The next day, she swears she had a Venti Mocha Frappuccino hangover. “I didn’t leave the house all day.”

Eventually she did venture out to meet some friends to see Slumdog Millionaire. But when they wanted to go for coffee afterwards…she politely declined.