Its answer was to call in PST, a company active in an important field known as re-marketing. Manufacturers, retailers and their intermediaries in a variety of sectors are increasingly turning to it as a way of reducing stockpiles.
With pundits increasingly convinced that the UK economy is in for a period of little growth, if not actual recession, it is expected that the demand for such a service will escalate. After all, the disappointing Christmas trading period experienced by many retailers showed how stocks can quickly build up to levels that are not easily reduced by traditional new year sales.
But John Meredith of Maidenhead-based PST says that demand for remarketing is high whatever the economic conditions. In recent years, that has been increasing because of the much-commented-upon pace of modern business.
Computer companies, like Wyse, are particularly susceptible to this as a result of the constant upgrading of features brought about by intense competition between manufacturers. And a good number of PST's client companies are in this sector.
In Wyse's case, the issue was what to do with the stocks of personal computers that the company had as a result of deciding to pull out of that part of the market.
Mark Jordan, vice-president for the company's European operations, says: "We didn't want product being dumped in the market with our name on it."
After PST had come up with a number of options, the two organisations agreed on which countries and which areas Twyford-based Wyse did not mind its discarded products being sold to and whether or not they should be sold with the company's name on them. The most important thing, he says, was ensuring that the company did not face a situation where customers had been offered stock more cheaply than would normally be the case.
But Mr Meredith says that has long been true of the computer industry is starting to affect other sectors, too. At the same time, the increasing emphasis on branding means that companies are loath to cheapen what they have so assiduously built-up by constantly offering some products at deep discounts.
The result is a demand for a service that companies will not typically perform themselves but out-source to companies such as PST. In some cases, the solution to overstocking is simple - for example, selling out-of- fashion lines of clothing to countries where consumers are less fashion- conscious.
But in the computer market, for instance, it is not just a case of selling PCs in countries where they are less freely available, but finding different applications for equipment. Something that might have very little retail value can perform a useful function in a factory, Mr Meredith adds.
Another solution in the computer field might be to bundle a collection of products into a package so that the branding is disguised and the price of each element is difficult to assess.
What re-marketers always bear in mind is that, while protecting the brand and established distribution channels are vitally important, companies do not call in a remarketing specialist unless they are looking to recover assets. And then the issue becomes time.
"If there's only a couple of days to go before the year end and a massive inventory of redundant stock is going to be an embarrassment on the books, then a quick cash sale is the answer," says Mr Meredith. "But given a little time, it is always possible to engineer a higher return."
One of the growing methods for improving returns is corporate barter - basically, a means by which a company swaps its stock for something it might want, typically advertising space or travel. Sometimes, companies do the swaps directly, but in the United States, in particular, intermediaries are growing up in a business that is worth about $8bn a year.
Whatever the route taken, the key is to be decisive. As Mr Jordan points out, management wants to liquidate stock. The longer it prevaricates, the more the price offered goes down.
"It's a tough decision to make," he says.