Trim characters in months to show just first three characters - excel

Question

I've written a loop that runs through a range containing month names and to trim any that are greater than three characters as I only need to see the first three ie: Jan instead of January.
The code below works in identifying the cells that contain the longer names but the LEFT function clears the cell rather than just removing the excess characters to show the first three only. Any idea what is amiss in the function? Help is much appreciated.
Many thanks.
Sub TrimMonth()
Application.ScreenUpdating = "False"
Dim rng As Range
Dim i, counter As Integer
Dim lastrow As Long
lastrow = ActiveSheet.Range("A1048576").End(xlUp).row
'Set the range to evaluate.
Set rng = Range("A2:A" & lastrow)
'initialize i to 1
i = 1
'Loop for a count of 1 to the number of rows in
'the range to evaluate.
For counter = 1 To rng.Rows.Count
'If cell i in the range contains more than 3
'characters then trim to 3 characters else increment i
If Len(rng.Cells(i)) > 3 Then
rng.Cells(i).Value = Left(Cells(i).Value, 3)
i = i + 1
Else
i = i + 1
End If
Next
Application.ScreenUpdating = "True"
End Sub

Answer 1

This code adds a formula to column B to return the three letter month text, then copies the values to column A before deleting the formula.
Sub TrimMonth()
Dim rDates As Range
With ThisWorkbook.Worksheets("Sheet1")
'Set reference to range containing month names.
Set rDates = .Range(.Cells(2, 1), .Cells(.Rows.Count, 1).End(xlUp))
'Add formula one column to right.
'This will convert the month name to a real date and then format it
'as three letter month text.
rDates.Offset(, 1).FormulaR1C1 = _
"=TEXT(DATEVALUE(""1-"" & RC[-1]),""mmm"")"
'Replace originals with values from formula.
rDates.Value = rDates.Offset(, 1).Value
'Clear formula.
rDates.Offset(, 1).ClearContents
End With
End Sub
Or to do it without adding the formula:
Sub TrimMonth()
Dim rDates As Range
Dim rCell As Range
With ThisWorkbook.Worksheets("Sheet1")
'Set reference to range containing month names.
Set rDates = .Range(.Cells(2, 1), .Cells(.Rows.Count, 1).End(xlUp))
'Convert each cell in range.
For Each rCell In rDates
rCell.Value = Format(CDate("1-" & rCell), "mmm")
Next rCell
End With
End Sub