Authorities want Jeremy Irwin and Deborah Bradley, missing baby Lisa's parents, to agree to separate interviews with the police to answer a list of tough questions they say they need answered.

It is now the fourth week of the investigation of missing baby Lisa Irwin. Kansas City Police Capt. Steve Young say authorities still have no major leads or suspects.

Attention by the police investigation and media alike has remained focused on Lisa's parents, Bradley, 25, and Irwin, 29.

We need them to sit down apart from each other, with detectives, and answer the tough questions detectives have for them concerning what they may or may not know about anything, who came and went [the night Lisa disappeared], Young told ABCNews.com. There's a whole list of things that they may know.

Young claims the parents have cooperated and answered other questions, but they have not sufficiently satisfied police demands. Authorities have expressed frustration with Bradley and Irwin, particularly following the alterations in Bradley's story.

Bradley admitted to drinking heavily on the night Lisa disappeared and says she may have even blacked out. She claims she did not see the baby after putting her to bed around 6:40 p.m., though she initially told the police she had put her daughter to sleep around 10:30 p.m.

The bottom line is detectives need to sit down with them unrestricted and they need to answer questions that we need answered, he said. Young claims that police have not had an unrestricted conversation with Bradley and Irwin since Oct. 8.

Joe Tacopina has criticized police, telling Good Morning America, that Bradley and Irwin have cooperated with the investigation by being interrogated and by allowing police to complete numerous searches of their home.

It really is maddening to me to listen to this police spokesperson come out there, and instead of informing the public -- and more importantly the family -- about leads and the status of the investigation and the manhunt, [Young] comes out and makes these statements, Tacopina told Good Morning America. And, quite frankly, [the parents have] done everything they've been asked to do...They have nothing to hide. They want answers.

Tacopina does, however, have restrictions on the kind of conversation he will allow baby Lisa's parents to have with the police. He claims that police have unfairly targeted Bradley, baby Lisa's mother, which doesn't build good faith in them. He says baby Lisa's parents are only willing to speak to police if they do not presume guilt before having sufficient evidence.

I am aware that he offered some vague criticisms of the police department, Young told ABC News. I think all reasonable people know that [we] are doing things and we know things that are not a matter of public record.

Bradley and Irwin's lawyers, Tacopina and Cyndy Short, however, believe police should focus their investigation on the man seen by three eyewitnesses carrying a baby in a diaper the night baby Lisa disappeared.

Mike Thompson, one of the eyewitnesses who says he saw a diapered baby with a man at 4 a.m. the night of Lisa's disappearance, told ABC News that police questioned him Monday.

Yesterday they showed me a paper with six pictures on it, Thompson said. And I picked out the man they had been showing pictures of.

The man in the photograph has been questioned by police, but the other two eyewitnesses do not believe he matches the description of the man they saw carrying a baby the night of Oct. 4.

No, I don't recognize him, the female witness told ABC News when shown the photo. He was tall and slender and, as far as his head, we thought he was bald.

Police, however, have refused to comment on the surveillance video found at a Kansas City gas station showing a man leaving a wooded area two miles from baby Lisa's home the night she disappeared. They also declined to comment Tuesday on the eyewitness reports, CNN said.

There have also been a number of reported sightings and tips regarding the 11-month-old's whereabouts, however, despite over 200 tips, authorities still have not found baby Lisa Irwin.

Police claim that a major difficulty in the case is Lisa's age, The Associated Press reported.

There is a kind of generic, cute little baby, little chubby cheek, bald-headed baby look, Ernie Allen, president of the Center for Missing and Exploited Children, told the AP. But our message to the public is, look at her picture. Really look at her in the eyes. Don't just see a cute little baby but look in the child's face. Like every human being she is unique. She is different. She doesn't look like every baby.

Baby Lisa was reportedly seen in California and then, last week, in Manhattan, Kan., but all of the reports have been false positives.

It would be far from reality to call this a cold case, Young told ABC News. We're still looking at everything.

However, there still remain no major leads or suspects in the investigation.

My fear is that we have missed this critical time to find this baby, Cynthia Short, an attorney for the parents, told KCTV. It really breaks my heart that we have been looking in the wrong direction, and as a result of that we might not get the happy ending that we want.

Baby Lisa's parents claim the 11-month old mysteriously disappeared from their home late Monday night or early Tuesday morning nearly three weeks ago. Irwin, an electrician, maintains that he returned from work around 4 a.m. Tuesday to discover baby Lisa missing. The parents say they searched frantically for baby Lisa early Tuesday morning, but found only the front door unlocked, a window opened, house lights turned on, and three cell phones missing.