Find the counterfeit coin from a bunch of eight coins using a simple balance scale only twice?

Question

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?

Answer 1

Split the 8 coins into 2 groups of 4 coins each.
1 of the groups carrying the fake coin will tilt the scales down.
now take the remaining 4 coins and again split them into 2 groups of 2
Now one of the 2 scales will tilt downwards again. This time take the topmost coin on either sides of the scale and on observation we can get the following possibilities.
1. The scale remains level ====> the coin taken from the downward tilted scale pan is the fake coin
2. The scale remains tilted ====> the coin left on the downward titled pan is the fake coin.

P.S. Strictly speaking the last part is a third weighing, hoping to see better answer from the community here !!!