There are important hoops the defense lawyer must navigate to compel judges to approve funding. The lawyer must first show the defendant is indigent and cannot afford to hire an expert on their own. The lawyer must also show the need for the expert involves some "significant factor" at the guilt/innocence or punishment phase of trial. This usually means the expert will be needed to develop certain types of evidence used in rebuttal or used to challenge the prosecutor's case. At times, the defense lawyer might need to demonstrate the legal admissibility of the evidence they are attempting to develop through the expert.
Next, the lawyer must present the expert's qualifications. This takes the form of a resume or vita. The judge will also need an estimate of the fees and expenses anticipated. I typically use the letter sent to me by the expert setting forth the proposed work, including trial testimony.
Lastly, the lawyer must state that neither he, nor his client, is sufficiently knowledgeable in the area of expertise for which they need assistance. I suppose if a lawyer was trained in forensic child psychology, the lawyer could serve as his own expert in a child abuse case. Sounds pretty silly, but still one of the necessary hoops we need to jump through.
Brazos County judges are usually very cooperative in granting funding when I apply. They might quibble over the cost at times, and sometimes I'll need to convince my expert to work for a bit less, but usually I get exactly what I ask for. Then, with the funding in hand for my expert of choice, I feel more confident in providing my clients with an effective defense.