investigation where the results are known from the very start as they are "ordered" (bribes, pressure etc.) - he who pays the piper calls the tune

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Note added at 1 hr (2006-04-14 06:42:11 GMT)
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a frame-up, a set-up

"greasy palms" investigation

So he knew better than to make a fuss by demanding an investigation, say, ... comprised only of sold-out courtiers equipped with greasy palms, ...
www.ragingblog.com/

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Note added at 1 hr (2006-04-14 06:43:42 GMT)
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I think there are a lot of greasy palms in them council offices ...
www.wiganworld.co.uk/forum/post.asp?method=ReplyQuote& REPLY_ID=53240&TOPIC_ID=4058&FORUM_ID=3

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Note added at 1 hr (2006-04-14 06:46:17 GMT)
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The Development of International Bribery Law
Формат файла: PDF/Adobe Acrobat - В виде HTML
... rule of law was above the influence of greasy palms. ... Committee investigation discovered a written record of the City’s instructions and an ...
www.transparency.ca/Readings/TI-G02.pdf

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Note added at 1 hr (2006-04-14 06:08:18 GMT)
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actually 'pre-programmed' (investigation)

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Note added at 2 hrs (2006-04-14 06:52:24 GMT)
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более эмоционально окрашенное слово (или выражение) -

PUPPET investigation

Буквально - "заказные сладости", но также и "заказная стряпня" (оплаченный обман). Мне кажется, в кавычках оно будет понятно ежу.

My first thought.

'You all know that I am innocent, that the engaged investigation lacks any proofs of my guilt...'

What if anything is the value of a 'neutral' as distinct from an 'engaged' investigation of mysticism and religious experience?
(A somewhat different sort of investigation, yet a good juxtaposition of 'neutral' (or objective) and 'engaged'.)

You will hardly find such usage with Google.
However I think this would deliver the meaning with all (or most) the accompanying connotations

Made-to-order means "по индив. заказу"

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Note added at 17 hrs (2006-04-14 22:35:17 GMT)
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You can also convey the meaning by saying "the investigation was ordered and paid for"

I think a more emotional word will weaken the sentence and sound unprofessional.

I suppose you'll have to decide what your context calls for.