Can AD9913 and AD9852 do multiple sequentially sweeps down?

In my FM modulator design, I use a direct digital synthesizer (DDS) to generate a frequency-modulated signal.
I have tested first demo design with the AD9958 which is perfect for FM modulation when modulation is performed by stepwise changing of the frequency tuning word (FTW0). But when i need to sweep between successive frequency steps the AD9958 and most other DDS ICs have a well-known drawback: they can not sweep down many successive times. For example, if we need sequentially sweep down between 100MHz ↓ 99MHz ↓ 95MHz ↓ 93MHz ↓ ...... DDS will only make instant jumps between the frequency steps, because S0 (FTW0) is always greater than E0 (FTW1). I found that it is possible to sweep down only after dummy sweep up: 100 ↑ 99,999   ↓   99 ↑ 98,999    ↓    95 ↑ 94,999    ↓    93 ↑ 92,999    ↓ ..... Thus, a series of downward sweeps becomes too complicated, because of the inserted dummy upward sweeps with S0>E0.
I also know about the sweep down using the second Nyquist zone. But this method is not suitable, because changing the direction of the sweep and, hence, of the Nyquist zone is not phase-continuous process, and leads to noisy phase transitions.
But fortunately there are DDS ICs which seems to have the inherent ability for the downward sweep.
According to the AD9913 datasheet,  the sweep direction is determined by the logic levels of the two independent pins: PS0 for sweep up and PS1 for sweep down.
Also, according to the AD9852/54 datasheets, they have two's complement DFTW.
So, can anybody confirm that the AD9913 and AD9852/54 can sweep down sequentially an arbitrary number of times?

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