This worked for me. Only the filtered (and thus, visible) rows are copied. The data was filtered with another macro. Hopefully it will helpful to others.
Sub Copy_Data()
Dim FirstBlankCell As Range
'Select source worksheet
Sheets("Source Data").Select
'Select and copy filtered rows
ActiveSheet.UsedRange.Offset(1, 0).SpecialCells _
(xlCellTypeVisible).Copy
'Select destination worksheet
Sheets("Destination Data").Select
'Paste filtered data
Set FirstBlankCell = Range("A" & Rows.Count).End(xlUp).Offset(1, 0)
FirstBlankCell.Activate
Selection.PasteSpecial Paste:=xlPasteValuesAndNumberFormats, Operation:=xlNone _
, SkipBlanks:=False, Transpose:=False
On Error GoTo 0
Set FirstBlankCell = Nothing
'Select source worksheet
Sheets("Source Data").Select
'Clears filters from source worksheet
ActiveSheet.ShowAllData
'Select destination worksheet
Sheets("Destination Data").Select
End Sub
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