Dear authors of this draft,

Some of us find it a very difficult paper to read and others,
clearly more introduced in the subject, find it a very good
paper. 
For the less introduced reader a qualitative explanation
why the strong phase difference \delta_D changes as indicated 
in Fig. 1 will be welcome. 
Also the disappointing sensitivity of our measurement 
of \gamma as compared to BABAR, Ref.[5] needs
more explanation; is it due to the accuracy of our values 
for x and y, or due to their central values?

The following comments about the text can be made:

Title:
One of us suggests:
"Constraints on CP violating observables by a Dalitz plot analysis
 of $B^\pm \rightarrow D K^\pm$ with $D \rightarrow K_S^0 \pi^+ \pi^-$ 
 and $D \rightarrow K_S^0 K^+ K^-$ decays" 
with the following arguments:
1- It is not clear if the analysis or the constraint on \gamma is
the main subject. As the analysis method is not new, is must be \gamma.
Unfortunately, our result for \gamma is not very significant.
We also give other CP violating observables, x_\pm and y_\pm,
for which we do pretty well.
2- "Model-independent" needs some explanation, it is not new, 
and it is not needed in the title.
3- The definition ($h=\pi,K$) is ugly in the title and does not 
make it much shorter compared to writing it out.
We also avoid $D \rightarrow K_S^0 \pi^+ K^-$ as a possible,
but wrong, interpretation.

Abstract:
Some improvements can be made.
"variation of the strong phase of the D": "strong phase difference \delta_D", 
                                variation as a function of what?
                                variation is called a quantity later on.
"ClEO-c": Why refer to CLEO-c in the abstract? Why CLEO-c and not CLEO?
          What strong phase "parameters"? 
Rephrase "first, second and third uncertainty".
Why no result for $\delta_B$?

Line 3-4: 
This is not clear. 
Maybe "When this weak phase is measured..."?

Line 9 and more: 
Are you using the definition of Dbar from the standard
LHCb template? 
We would expect a longer bar on the D (i.e use overline)
and on the A in Eq.(1).

Lines 19-21:
Remove ", which can be performed ... systematic uncertainty" here. 
This is explained better in lines 38-44 and repeated in
lines 50-52.

Lines 34-35: 
"As CP violation ... it is valid to write ...". 
Don't use 'extremely' or 'it is valid'. 
Our suggestion: 
"Both in D0 mixing and in Cabibbo favoured D decays CP violation 
is expected to be negligible [15]. 
We will assume A(m1,m2) = Abar(m2,m1)." 
Can this be combined with the remark in line 57-60?

Remove the hyphen in "strong-phase difference". Also at other places.
("strong difference" is not usual and also without hyphen "strong" will be
always related to "phase".)

Put a \times, \cdot, or a second square root between the two integrals 
in the denominator of Eq.(2) to distinguish the two integrals better.

Line 48: 
Change "an uncertainty is assigned which" to
"an uncertainty is assigned that".

Lines 50-52:
See comment on lines 19-21.

Line 75, Figure 1:
Add a diagonal line as the colour coding does not allow to
distinguish bin -1 from bin 1.

Line 100:
Be more precise!
Change "~ 10^6 events are available for final analysis" to
"about 1.3(?) 10^6 B decay events enter the analysis in which
1200(?) are selected with the B^\pm -> DK^\pm, D->K^0_Sh^+h^- decay chain.
(A more precise number than \approx 10^6 should be available.
The number of 1200(?) selected events in Fig.2 would be good
to compare with the 213+441 signal events given in Table 1.

Line 101: 
"each of the modes" is not very clear. 
Maybe "events for each of the modes".

Line 112: 
Change "vital" to "important" or "useful".
We don't think anyone's life is at risk.

Line 113: 
Change "For each B candidate a production vertex is designated." to
"To each B candidate a reconstructed production vertex (PV) is assigned."
(The sentence is now also used to define PV.)

Line 114: 
Change "This is the PV that has the smallest impact parameter \chi^2 
with respect to the B flight direction" to 
"This is with more collisions per bunch crossing the PV for which the
reconstructed B trajectory has the smallest \chi^2 in the impact parameter 
fit."
(There is no shortest distance, IP, to a direction only.
 This seems to be what we do, although an additional cut on IP itself would 
 make more sense.)

Lines 131-132: 
Change "the alignment between" by "the angle \theta between" and 
add "(\cos{\theta}>0.99)" after "selection".

Line 134:
Replace "and so a window of \pm 25" by "and a common window of \pm 25".

Line 183: 
"The random track component" sounds odd. 
The tracks are not random, only the combination is. 
Write "The random track combinations are modeled by". 

Line 188: 
Remove the spurious space between D and K. 
Use \xspace in your macros.

Table 1: 
Why is there strictly no DK component in D\pi?
Replace the slash ('/') by a dash, or just remove it.

Lines 216-220: 
This sentence is not clear. 
And it contains at least one error: 'is' instead of 'in'. 
'R' is undefined.

Lines 257-259:
"The yields of all the background contributions in each bin 
are free parameters, apart from certain bins where a very low
contribution is observed, in which case they are fixed to zero." 
- How do you know that the contribution is low, unless you fit for it? 
- What do you gain by fixing it to zero?

Line 273:
Replace "Also shown are the total systematic uncertainties, discussed
in Sect.6." by
"The LHCb related systematic uncertainties are discussed in Sect.6.".

Line 279: 
"The two sets are compatible within ... uncertainties."
This seems to be a superfluous sentence which can be omitted.
Here it looks as if we want to hide some kind of problem.
The most obvious thing to do would be to give the results for
D to KSK+K- in a 4th column.

Line 281-284: 
"The expected signature of a sample that exhibits CP violation 
is that the two vectors defined by the coordinates (x-,y-) and (x+,y+) 
should both be non-zero in magnitude, but have different phases. 
The data show this behaviour, 
but are also compatible with the no CP-violation hypothesis." 

You cannot have both. If the data are compatible with no CP violation, 
then the data do NOT show that (x-,y-) and (x+,y+) are both different 
from zero. 

Replace it by "The presented data are compatible with both the existing
evidence for CP violation and with no CP violation."

Line 290, 292 and Fig.6: 
Replace "effective bin number" by "modified bin number"i
or "B charge dependent bin number".
There is no good reason for the word "effective".

Line 301: 
Remove "although this is less favoured that the fit result, as expected." 
The probability to find a result that is less favoured than that 
with a chi2 of 26.1/20 is 16%. That makes this a very normal result. 
Therefore, we shouldn't say that it is 'less favoured' than
another fit result. 

Figure 5 is ugly and needs to be redone.
Rob Lambert can tell you how to make beautiful contours.
The identification of the two contours with the B charge should be better
explained in the caption.

Table 4: 
"Total LHCb internal" sounds strange. 
Use "Total LHCb related systematic".

Line 350: 
Replace "feasible" by "possible".

Line 429:
Replace "800 ... both to... and ... 2011 and analysed to" by 
"654 ... either to ... or ... in 2011. These events are analysed to".
(Repeat in the Conclusions a number that has been used before.)

Figure 7 is ugly and needs to be redone.

Line 435:
Replace "the world average of results of previous experiments [15],
although the uncertainties ... are large." by
"the results of previous experiments [15]. The uncertainties ... are large."
(No need for world average unless you give its value.
Do not use "although".) 

Line 437-439:
"More stringent constraints are expected when these results are combined 
with those from related LHCb studies performed with the same data set [1]
... larger samples"
is not clear for the first part.
Replace it by:
"The prospects are good for improving the significance with more data as our 
statistical uncertainties for x_\pm and y_\pm are already competitive.
More stringent constraints are also expected when our CP violation studies
on other D decay modes as in Ref.[1] are combined".