The most energy-efficient models of furnaces available are typically those that have received an ENERGY STAR® certification. According to the U.S. Environmental Protection Agency (EPA), these furnaces meet strict guidelines for energy efficiency, and can provide significant energy savings compared to standard models. The specific models and brands that qualify for ENERGY STAR® certification can vary depending on factors like regional climate and fuel type, but some of the top options include:

1. Lennox SLP98V: This gas furnace offers up to 98.7% AFUE (Annual Fuel Utilization Efficiency) and has received the ENERGY STAR® Most Efficient 2020 award.

2. Trane XC95M: This gas furnace offers up to 97.3% AFUE and has received the ENERGY STAR® Most Efficient 2020 award.

3. Bryant Evolution® 987M: This gas furnace offers up to 98.3% AFUE and has received the ENERGY STAR® Most Efficient 2020 award.

4. Carrier Infinity® 98 Gas Furnace: This gas furnace offers up to 98.5% AFUE and has received the ENERGY STAR® Most Efficient 2020 award.

It’s important to note that while these high-efficiency furnaces may come with a higher upfront cost, the energy savings over time can offset the initial investment. Additionally, some states and utility companies offer rebates or incentives for purchasing energy-efficient HVAC equipment, so be sure to check for available programs in your area.