Retailers that use Square Inc.’s mobile point of sale acceptance service now have an option to reward their loyalty customers who use the Pay with Square app.

The new loyalty features enable consumers to electronically enroll in a retailer’s Square-backed rewards program to receive discounts. For example, a retailer can offer a first-time customer a discount, extend discounts to regular customers and reward frequent purchasers. Retailers set up the discounts via Square’s online dashboard and can choose percentage discounts or dollar amounts, a Square spokeswoman says.

Consumers search a directory of retailers that accept Square to find those with rewards programs.

Square launched Pay with Square in March. After registering as a user, consumers link their payment cards to the app, which they can then use to complete an in-store transaction.

The consumer directs the merchant to put the purchase on her tab. The consumer’s name and photo automatically appear on the merchant’s Square Register app, the merchant confirms the consumer’s identity and the goods purchased are charged to the payment card tied to the consumer’s Square mobile wallet.

The allure of offering a loyalty program with a mobile POS app may not appeal to all retailers, especially smaller ones drawn to Square because of its lack of a typical merchant contract and simplified pricing of 2.75% per swiped transaction, says David Fish, senior analyst at research firm Mercator Advisory Group Inc. “Loyalty and offers are a key part of a mobile wallet offering,” Fish says. “I’m just not sure merchants at the mom-and-pop level are easily convinced that this is for them. It’s a different value proposition than enabling a micro-business to accept cards through a smartphone.”

Square says more than 75,000 merchants accept Pay with Square.