When recording the deselection of the "(Blank)" items I get an explicit mention of all items.
ActiveChart.PivotLayout.PivotTable _
.PivotFields("[Table1].[Field1].[Field1]").VisibleItemsList = _
Array("[Table1].[Field1].&[Item1]", _
"[Table1].[Field1].&[Item2]", _
"[Table1].[Field1].&[Item3]", _
"[Table1].[Field1].&[Item4]", _
"[Table1].[Field1].&[Item5]", _
"[Table1].[Field1].&[Item6]")
But I can't mention the items since I don't know them beforehand (and they are located in the data model).
The code should be along the lines of:
With ActiveChart.PivotLayout.PivotTable
.PivotFields("[Table1].[Field1].[Field1]").VisibleItemsList = Array("")
.PivotFields("[Table1].[Field1].[Field1]").PivotItems("(blank)").Visible = False
End With
EDIT: Apparently, .PivotItems("(blank)").Visible = False
should be doing exactly what I need, but it is not... (Runtime '1004': Unable to get the PivotItems property of the PivotField class)