VBA: Run-time error 3001 Arguments Are Of The Wrong Type... when setting ADODB.Command object members

This forum post saved my day.
I was trying to run Oracle stored procedure with output parameters from Excel VBA with the following piece of code:

Dim cmd As Object
Dim resultSet As Object
Set cmd = CreateObject("ADODB.Command")
With cmd
    .CommandText = "PK_AUTH.LOGON"    
    .NamedParameters = True
    .Parameters.Append .CreateParameter("login", adVarChar, adParamInput, 50, login_)
    .Parameters.Append .CreateParameter("pass", adVarChar, adParamInput, 50, pass_)
    .Parameters.Append .CreateParameter("ldb", adVarChar, adParamOutput, 50)
    .Parameters.Append .CreateParameter("pdb", adVarChar, adParamOutput, 50)
    .CommandType = adCmdStoredProc
    .ActiveConnection = GetConn_()
    Set resultSet = .Execute
    ldb_ = .Parameters.Item("ldb")
End With

And I always got Run-time error 3001 'Arguments Are Of The Wrong Type, Are Out Of The Acceptable Range, or are in conflict with one another' upon invocation of

.CommandType = adCmdStoredProc

or

.Parameters.Append .CreateParameter(...)

no matter which statement I placed first.
After fighting for a while I found this post that stated that error is fired because of late binding of library references, so VB simply did not know of adCmdStoredProc and other constants
That meant that this error has nothing to do with ADODB or Ole or, I just said that it does not know the value of constant. Not very informative in fact...
So, I simply added

Const adVarChar As Long = 200
Const adParamInput As Long = &H1
Const adParamOutput As Long = &H2
Const adCmdStoredProc As Long = &H4

to the Sub header and everything worked fine. Constants are defined in c:\Program Files\Common Files\System\ado\adovbs.inc