Worksheet Change: Data In A Range, And Hits The "delete" Key Once

I have code in Worksheet_Change, and it works great when a user is filling in the data. When the user deletes data one row at a time, it also works. However, what winds up happening, is the user selects all their data in a range, and hits the "delete" key once, and then I get an error. How can I check whether or not the target is multiple rows and columns?

Private Sub Worksheet_Change(ByVal Target As Range)
Application.EnableEvents = False
If Target.Column = 1 And Target.Row > 15 Then
If Target.Value < 1000 And Target.Value <> "" Then
'My logic goes here
End If
End If
Application.EnableEvents = True
End Sub