Alisa Maier's homecoming Thursday in Louisiana, Mo., was a joyful gathering of cheers and hugs on the front lawn that she was snatched from three days before.

In St. Louis, police offered more details on the hunt for her kidnapper - and how the man's purchase of cigarettes helped to give away his identity.

Alisa, 4, was abducted about 8 p.m. Monday and released 26 hours later at a car wash in Fenton, a southwest suburb of St. Louis, 80 miles south of Louisiana.

Police expressed confidence Thursday that the kidnapper was Paul S. Smith, 38, a convicted sex offender who fatally shot himself Wednesday as deputies approached him in Hawk Point. A relative said Alisa and her brother, Blake, 6, also identified Smith when his face was shown on TV.

When Lincoln County deputies arrived at Smith's Hawk Point address, he was spraying his dark-colored, 19-year-old Mazda with silver paint. Blake and two witnesses in Fenton had described seeing a dark-colored, beat-up car.

But the key to finding Smith was a trip he took to the Walmart in Troy, Mo., to buy clothes for Alisa and cigarettes for himself, police said.

St. Louis County Police Chief Tim Fitch said that after Alisa was recovered, investigators traced her new clothing to the store. Fitch said Smith appeared on a surveillance video making the purchases, but the image wasn't clear.

Smith paid in cash, Fitch said, but gave the clerk his birth date to buy cigarettes.

"All we had was a date of birth and a photo," Fitch said.

That was enough to identify sex offender Smith as a "person of interest" and spur the deputies' visit to his cabin on Route D in Hawk Point.

Hawk Point and Troy, both in Lincoln County, are 10 miles from each other and 40 miles south of Louisiana, a town of 3,900 residents on the Mississippi River. Alisa's home, on North Carolina Street, is barely a block away from the Louisiana City Hall and police station.

worth a somersault

Alisa arrived home at 1:25 p.m. Thursday to the cheers of about two dozen relatives and friends. She wore a red shirt with an American flag on the front, red pants and pink flip-flops, as her mother, Kimberly Harrison, walked her to the front door beneath a large banner saying, "Welcome Home Alisa."

Her father, David Maier, followed them with overnight bags. Asked about the ordeal, Maier said: "You don't want to know. I've been numb this whole time this has been going on."

As to his daughter, he said: "She's happy. I'm not pushing her to say anything."

Her mother said simply: "I really missed her. I'm just glad she's home right now."

As the crowd bubbled with happy noise, Alisa bounded back onto the porch, ready to play. A cousin, Carissa Doyle, grabbed her for a hug.

Since Alisa was reunited with her family early Wednesday, the family had been in seclusion at an undisclosed motel in the St. Louis area. As relatives awaited the homecoming, a youngster's front flip inspired Alisa's grandfather Roy Harrison to do a somersault.

On Wednesday, after word of Alisa's recovery, he had said, "I'd do a back flip if I could, but I'm just too dadgum old." His quote was reported from coast to coast.

Angela Reddick, a great-aunt, said of Smith: "I wish we could have faced him in court. It's justice in a way, because now he's facing his maker."

Great-grandmother Mary Foiles sought to find something redeeming in Smith's decision to free Alisa at Fenton Car Wash. "I believe that man had enough good in him that God could touch him," Foiles said. "Either that, or he was so afraid, he let her go. Or maybe both."

seeking answers

Earlier Thursday, Fitch outlined the police case to reporters in Clayton. He said they had obtained search warrants on Smith's residence, car and cell phone. Police spent the day at the Hawk Point property, combing for clues.

"We have recovered evidence to lead us to believe that he is the one who abducted Alisa," Fitch said.

Smith shot himself at 4:30 p.m. Wednesday as the three deputies approached. He died six hours later at St. Joseph Health Center in St. Charles.

Fitch said officers believe that Smith, who lived in a cabin at the Hawk Point address, acted alone. They don't know why he picked Alisa or went to Fenton.

County police Lt. Col. Terry Roberds said there was no medical evidence that Alisa had been abused, nor has she suggested that in interviews. Roberds said strong public interest and news coverage probably caused Smith to release her.

"With his history, you can only assume what would have happened had he had her longer," Roberds said.

Smith served 11 years in prison for sexually abusing a boy in Rolla, Mo., and police have begun looking into any connection between him and other missing-children cases.

Roy Harrison, the grandfather, said Alisa and Blake also identified Smith. He said Alisa was watching a TV newscast with her parents in St. Louis when she saw a picture of Smith.

"Without prompting, she said, ‘He cut my hair,' " Harrison said.

Alisa's hair was short when she was found. Police assume Smith cut her hair and bought clothes to conceal her much-publicized identity.

Harrison said Blake had the same reaction when he saw Smith's picture. Harrison praised his grandson for giving a solid description to police.

"I think he was right on," Harrison said.

Kim Bell, Tim O'Neil and Nicholas J.C. Pistor of the Post-Dispatch contributed to this report.