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Copiapo, Chile (CNN) -- Rescue crews in Chile will begin at midnight Tuesday -- and perhaps even earlier -- to free the 33 miners trapped for more than two months nearly half a mile below ground, Chile's mining minister said Monday.

"We are hoping to initiate the rescue beginning at zero hours on Wednesday," or 11 p.m. ET Tuesday, Laurence Golborne told reporters outside the mine. Though it may come even sooner, he said, "We're going to take all the time necessary to assure that the plans are adequate."

That decision was made after the rescue capsule, called Phoenix 1, was lowered overnight to 610 meters (about 2,000 feet), 12 meters short of where the men are trapped, he said. "It fit very well," he said. "Not even dust fell inside."

Asked why the capsule was not lowered all the way into the mine, Golborne said, "We could not risk that somebody might jump in."

The extraction cannot begin immediately because the concrete base built for the winch system must first harden, he said.

On Monday afternoon, Alejandro Pino, regional manager of the Chilean Safety Association, presented to reporters the gear that the miners will use once their rescue begins.

Each miner will receive green coveralls embroidered with their names, as well as fresh pairs of socks and underwear. The outfits are made of material designed to resist moisture, Pino said.

He urged reporters to allow the miners, as they come up, to spend time alone with their families.

"Let them have long embraces," he said.

In addition, each miner will also be given a blanket embroidered with their names. "They're going to be able to keep it for their homes," he said.

During their conversation Monday, the miners told Pino, "We're anxious, but tranquil," he said.

The miners' personal trainer, Jean Romagnoli, said the miners will wear a special belt that will monitor their vital signs during their ascent, which will be monitored from a computer on the surface.

"I don't need to see (the miner in the rescue capsule) to know exactly what is going on with him," he said.

All of the miners appear to be in good physical and emotional shape.

"We are extraordinarily content," Minister of Health Jaime Manalich said.

Earlier Monday, workers cheering "Viva Chile" completed the installation of steel tubing to reinforce the path that rescuers plan to use to hoist the trapped miners to the surface.

About 56 meters of sheet metal has been put in place to line the tunnel, according to Andre Sougarret, the rescue leader. Plans for a longer tube were aborted after they were deemed not necessary, he said.

Officials have said that the most technically adept miners will be the first to ascend the rescue shaft so that they can help with their own rescues should any problems arise. They will be followed by miners who have health concerns, such as diabetes or heart conditions. The miners judged to be emotionally strongest will go last.

When he told the miners through video conference that they would have to choose their order of rescue, there was no shortage of volunteers to go last, Manalich said.

"They continue to have an admirable attitude," he said.

Beginning six hours before the rescue starts, the miners will be switched to a diet of liquids, vitamins and minerals ahead of their trip to the surface. Each trip is expected to take about 15 minutes.

The change in diet is one way that officials are trying to mitigate some of the challenges associated with the rescue. These include concern about the miners feeling lonely, dizzy or panicked.

Authorities plan first to lower a doctor and a rescuer into the chamber, Manalich said earlier.

Once the men have been extracted, they will undergo about two hours of health checks at a field hospital set up at the mine. They will then be flown by helicopter to a hospital in the town of Copiapo -- approximately a 15-minute flight.

Miners who are healthy enough will be allowed to visit briefly with family members in a reunion area before being taken to the hospital.

Health officials have increased the miners' physical activity in recent days to gauge how they can handle the stress of being removed.

The overall response has been good, though some miners have exhibited anxiety or have had minor cardiac issues, Manalich has said.

The miners have been in contact with the outside world through a small bore hole that sends them food, water and other supplies and necessities.

CNN's Karl Penhaul and Patrick Oppmann contributed to this report.