Sovran Self Storage’s properties are filling up, and that’s causing the Amherst-based company’s profits to shoot up.

Sovran’s earnings jumped 31 percent as the company’s Uncle Bob’s self-storage facilities ended the second quarter with occupancy levels that topped 90 percent.

With demand up, Sovran also was able to raise rents by an average of 3.6 percent and slash the value of the move-in discounts that the company often offers customers who are moving in to one of its stores.

“We really like where we are right now,” said David Rogers, Sovran’s chief executive officer, during a conference call Thursday.

Sovran’s earnings jumped to $29.5 million, or 94 cents per share, from $22.4 million, or 77 cents per share, a year ago, easily topping the 90 cents per share that analysts were expecting. Shares rose $1.04, to $70.14 on Thursday.

“The summer season has been a good one,” Rogers said. “We’ve been able to gain pricing power by increasing rates and reducing discounts.”

As a result, Sovran increased its earnings forecast for this year by about 4 percent. Sovran said it expects its earnings during the current quarter to range between 96 cents and 98 cents per share, slightly better than the 95 cents per share that analysts were expecting.

For the year, Sovran said it expects to earn between $3.70 and $3.74 per share, which would easily top the $3.61 per share that analysts are forecasting. The company in May had estimated that it would earn $3.56 per share.

Much of the strength stemmed from a shrinking supply of available units at Sovran’s stores. Occupancy levels at the 471 stores that Sovran manages in 25 states that have been open for at least a year jumped to 91 percent at the end of June, up from 87.7 percent a year ago.

“Demand is up,” said Edward Killeen, a Sovran executive vice president.

With plenty of customers looking to rent self-storage facilities, Sovran was able to raise its average rents to $10.75 per square foot, up from $10.38 a year ago.

And the company also reduced the value of the concessions it offers to many customers who are beginning to rent one of its self-storage units. Sovran offered concessions to just 48 percent of its new customers during the second quarter, down from 70 percent a year ago, and the value of those discounts also dropped to an average of $55, compared with $73 a year ago.

“We continue to rent. We continue to add occupancy. Therefore, we should be able to continue to drive down concessions a little bit,” Killeen said.

That trend continued into July, with same-store occupancy rates rising to 91.7 percent from 88.7 percent a year ago, and average rents jumping by 8 percent to $11.48 per square foot from $10.63 per square foot a year ago.

Sovran said the company, which didn’t buy any properties during the spring, has contracts to buy three additional stores, including two on Long Island and one in Colorado, for a total purchase price of $27.9 million. Sovran executives said they still expect the company to make about $150 million in acquisitions this year, with much of the activity likely to occur during the fourth quarter.