Excerpt: Suzanna and her puppy Nikki had more than 100 cactus needles covering their bodies when they were rescued. The two long-haired dachshunds were abandoned in the county for hours before a couple driving by saw them from the road. The dogs had done nothing wrong; there just wasn't enough money for their family to care for them.

With the economy's recent downturn, some owners are finding they cannot afford to provide for their dogs and, subsequently, give them up.

"People are dealing with the economic crunch, and they're getting rid of what they absolutely don't have to have, and pets fall into that category, unfortunately," said Anne Burkett , president of Austin German Shepherd Rescue .

Within the past year, the number of dogs being dumped at the...