Faye Hicks has a problem. Actually, the adoption specialist at Franklin County Animal Shelter has about 21 problems -- soft, wide-eyed problems with high-pitched voices, claws like needles and lashing tails.

They are cats and kittens, and they have problems, too: They are homeless, and if they don't find somewhere to go, they could be euthanized.

June is adopt-a-kitten month, which ties in with "kitten season," the warm-weather months when cats give birth. It's also the time of year when animal shelters across the Roanoke Valley must deal with the summer's cutest, fluffiest problem: too many kittens, not enough cages.

The Franklin County shelter has 20 cats in foster homes and three empty cages. Animals at the facility range from four newborns to adults.

"We can fill up just in a matter of no time," Hicks said. "It can happen so quickly."

Most of the cats at Franklin County's shelter are strays, but some are "owner relinquished"-- pets dropped off because people can't or don't want to care for them any longer.

The shelter keeps the animals for as long as possible, but if it runs out of space, the animals face a tranquilizer and then lethal injection.

"We do everything we can," Hicks said. "Sometimes we run out of people, run out of resources."

Shelters across the valley say the problem lies with people who don't assume responsibility for their cats. State law says ownership begins when a person acts as custodian of an animal, said Lt. Bill Bandy of Salem Animal Shelter. Feeding strays falls in this category.

"It's really like, 'Why don't you take the extra step and give it a name?' " Bandy said. "Take the extra step and get it its vaccines."

Feeding cats is part of the problem. When cats are well-fed, they are more likely to reproduce, exacerbating the problem of kitten season. Feeding a cat is a kind gesture, Bandy said, but not necessarily a responsible one.

Responsible pet owners spay or neuter their cats, said Kathy Perdue, director of marketing and development at the Roanoke Valley Society for the Prevention of Cruelty to Animals. She said an unspayed female and her offspring can produce 420,000 cats in seven years. Cats have three or four litters a year and can begin reproducing at 6 months old. They can also become pregnant while nursing.

Virginia law requires people who take animals home from shelters to get them neutered 30 days after adoption. Violators face up to $150 in fines. Some shelters neuter animals themselves.

The Roanoke Valley SPCA currently holds 32 adult cats and 16 kittens, with another 51 felines coming in over the next two weeks from foster homes. Fostering frees up space at the shelter and helps socialize cats and kittens, Perdue said, so they acclimate easily to new homes.

"Way too many cats are losing their lives because they don't have homes," Perdue said. "Anyone who says to me, 'Oh, I already have a cat,' I say, 'You have one? Only one? When eight are going to die?' "

The hardest part about taking mother cats and kittens back from foster homes is knowing the mother may linger in the shelter while her kittens find homes quickly, she said.

"Whenever we have kittens, it seems people instinctively know," she said.

The Roanoke Valley SPCA calls itself a no-kill shelter because it keeps animals until they find homes. Staff at the Franklin County Animal Shelter said that merely means some other shelter will wind up with the cats.

"The truth is you're passing the buck on to somebody," said Capt. Marvin Woods of Franklin County Animal Control. "We could easily put a sign up that says no-kill, and we would only be taking adoptable animals. And where do the other ones go?"

Salem Animal Shelter tries to hold animals for 60 days, but if space is tight, euthanasia makes room for newcomers. Bandy said putting animals down is a difficult but necessary procedure.

"To me, I would rather see this cat euthanized in the shelter than go into a home where it's not going to be spayed or neutered and produce litter after litter," he said. "I'd rather euthanize one than 30. There's worse things that can happen to pets than euthanasia."

Kittens are no exception. The fragile creatures are sometimes too sick or weak to put up for adoption.

"We sometimes euthanize kittens," Bandy said. "It's hard. Euthanasia bothers all of us."