The Tax Treaty leaves open areas for interpretation, but since a lump sum is defined as 100% then presumably any amount less than 100% would still qualify.
That is, it can be interpreted that any amount less than the 100% lump sum does qualify as periodic payments regardless of what percentage of the account each payment represents.
An analysis of the tax treaty treatment of pensions is available at http://www.weil.com/news/pubdetail.aspx?pub=8292
"Benefits Taxable in Country in Which Individual Resides
Article 17 of the Tax Treaty provides, as a general rule, that pension benefits paid to an individual will be taxable only in the country in which that individual then resides. However, the country in which the individual then resides must exempt from tax any amount of such pension benefit if such benefit would be exempt from taxation in the country in which the pension plan was established. For example, a distribution from a USbased Roth IRA to a UK resident would be tax exempt in the UK to the same extent it would be exempt from tax in the US if distributed to a US resident. In addition, a transfer by a UK resident of US pension funds between pension plans, e.g., a rollover, would continue to be exempt from tax, as it is not deemed distributed
for US or UK purposes.
Lump Sum Exception.
An exception to the above rule concerns lump sum distributions. Lumpsum payments to an individual - regardless of where the individual resides - will be taxable in the country where the pension plan is established. However, due to the Tax Treaty's "savings clause," the country where the individual resides is still
able to tax the lump sum distribution. This exception was enacted to avoid the
lump sum distribution being exempt from tax in both the US and the UK, because
the UK does not tax lump sum pension distributions, and individuals who
anticipated receiving a lump sum distribution from a US pension plan were
previously able to avoid US withholding tax on such distribution by establishing
residence in the UK for the year in which the distribution was to be received.
The impact of the savings clause, though, allows the US to tax such
distributions from a UK pension plan to a US resident."
So long as you are not avoiding paying tax in both countries any series of payments is allowable.
There is no set amount or percentage that is required or prohibited to be distributed so long as the total is distributed within five years.
Hope this clarifies that the rules are in place to prevent not paying tax to either country on the distributions.