diff --git a/docs/fully_coherent_search_using_MCMC.md b/docs/fully_coherent_search_using_MCMC.md
index 236b628de9286fbb689d94649d03d84208896d57..3e0de8cd9e4df903243c3017cddada426f419f91 100644
--- a/docs/fully_coherent_search_using_MCMC.md
+++ b/docs/fully_coherent_search_using_MCMC.md
@@ -2,8 +2,8 @@
 
 In this example, we will show the basics of setting up and running a MCMC
 search for a fully-coherent search. This is based on the example
-[fully_coherent_search.py](../example/fully_coherent_search.py). We will run
-the search on the `basic` data generated in the
+[fully_coherent_search_using_MCMC.py](../example/fully_coherent_search_using_MCMC.py).
+We will run the search on the `basic` data generated in the
 [make_fake_data](make_fake_data.md) example.
 
 First, we need to import the search tool, in this example we will use the
@@ -83,7 +83,7 @@ mcmc.run()
 
 This produces two `.png` images. The first is the position of the *walkers*
 during the simulation:
-![](img/fully_coherent_using_MCMC_walkers.png)
+![](img/fully_coherent_search_using_MCMC_walkers.png)
 This shows (in red) the position of the walkers during the burn-in stage. They
 are initially defuse (they start from positions randomly picked from the prior),
 but eventually converge to a single stable solution. The black is the production
@@ -99,7 +99,7 @@ To get posteriors, we call
 mcmc.plot_corner()
 ```
 which produces a corner plot
-![](img/fully_coherent_using_MCMC_corner.png)
+![](img/fully_coherent_search_using_MCMC_corner.png)
 illustrating the tightly constrained posteriors on `F0` and `F1` and their
 covariance. Furthermore, one may wish to get a summary which can be printed
 to the terminal via
diff --git a/docs/fully_coherent_search_on_glitching_data.md b/docs/fully_coherent_search_using_MCMC_on_glitching_data.md
similarity index 96%
rename from docs/fully_coherent_search_on_glitching_data.md
rename to docs/fully_coherent_search_using_MCMC_on_glitching_data.md
index 4332aeb943082322ff823b5cab092df97add6a25..04ff8af78f0cbe7b25db64e0ced2296170f70277 100644
--- a/docs/fully_coherent_search_on_glitching_data.md
+++ b/docs/fully_coherent_search_using_MCMC_on_glitching_data.md
@@ -1,7 +1,7 @@
 # Fully coherent search on glitching data using MCMC
 
 This example applies the basic [fully coherent
-search](fully_coherent_search.md), to the glitching signal data set created in
+search using MCMC](fully_coherent_search_using_MCMC.md), to the glitching signal data set created in
 [make fake data](make_fake_data.md]). The aim here is to illustrate the effect
 such a signal can have on a fully-coherent search. The complete script for this
 example canbe found
diff --git a/docs/img/fully_coherent_on_glitching_data_corner.png b/docs/img/fully_coherent_on_glitching_data_corner.png
deleted file mode 100644
index bfb47e5b294063edc8b3576ca7115495a053831d..0000000000000000000000000000000000000000
Binary files a/docs/img/fully_coherent_on_glitching_data_corner.png and /dev/null differ
diff --git a/docs/img/semi_coherent_glitch_search_corner.png b/docs/img/semi_coherent_glitch_search_corner.png
deleted file mode 100644
index 870925ceb1983be9010fdd6c6245ec6a5ae557b2..0000000000000000000000000000000000000000
Binary files a/docs/img/semi_coherent_glitch_search_corner.png and /dev/null differ
diff --git a/docs/img/semi_coherent_two_glitch_search_corner.png b/docs/img/semi_coherent_two_glitch_search_corner.png
deleted file mode 100644
index 2f03f7a926d0712d50ab7b7a8aaffb5f9e5938fb..0000000000000000000000000000000000000000
Binary files a/docs/img/semi_coherent_two_glitch_search_corner.png and /dev/null differ
diff --git a/examples/fully_coherent_search_on_glitching_data.py b/examples/fully_coherent_search_using_MCMC_on_glitching_data.py
similarity index 65%
rename from examples/fully_coherent_search_on_glitching_data.py
rename to examples/fully_coherent_search_using_MCMC_on_glitching_data.py
index fbb8b349d66f5decac87e82034b0352ed1397aea..9e5992a01c759a8be0593a2b59459dbbaf774fdb 100644
--- a/examples/fully_coherent_search_on_glitching_data.py
+++ b/examples/fully_coherent_search_using_MCMC_on_glitching_data.py
@@ -1,5 +1,4 @@
 from pyfstat import MCMCSearch
-import numpy as np
 
 F0 = 30.0
 F1 = -1e-10
@@ -12,9 +11,8 @@ tstart = 1000000000
 duration = 100*86400
 tend = tstart + duration
 
-theta_prior = {'F0': {'type': 'unif', 'lower': F0-5e-5,
-                      'upper': F0+5e-5},
-               'F1': {'type': 'norm', 'loc': F1, 'scale': abs(1e-6*F1)},
+theta_prior = {'F0': {'type': 'unif', 'lower': F0-1e-4, 'upper': F0+1e-4},
+               'F1': {'type': 'unif', 'lower': F1*(1+1e-3), 'upper': F1*(1-1e-3)},
                'F2': F2,
                'Alpha': Alpha,
                'Delta': Delta
@@ -25,11 +23,11 @@ log10temperature_min = -30
 nwalkers = 500
 nsteps = [100, 100, 100]
 
-mcmc = MCMCSearch('fully_coherent_on_glitching_data', 'data',
+mcmc = MCMCSearch('fully_coherent_search_using_MCMC_on_glitching_data', 'data',
                   sftfilepath='data/*_glitch*.sft',
                   theta_prior=theta_prior, tref=tref, tstart=tstart, tend=tend,
                   nsteps=nsteps, nwalkers=nwalkers, ntemps=ntemps,
-                  log10temperature_min=log10temperature_min, scatter_val=1e-6)
+                  log10temperature_min=log10temperature_min)
 mcmc.run()
 mcmc.plot_corner(add_prior=True)
 mcmc.print_summary()
diff --git a/examples/make_fake_data.py b/examples/make_fake_data.py
index ede4cbe8006e256acdbe167f1e8cdece268be1a6..1cc195420991a170af1cce1c3e61c86eac09f5c6 100644
--- a/examples/make_fake_data.py
+++ b/examples/make_fake_data.py
@@ -27,7 +27,7 @@ data.make_data()
 
 # Next, taking the same signal parameters, we include a glitch half way through
 dtglitch = duration/2.0
-delta_F0 = 0.4e-5
+delta_F0 = 4e-5
 delta_F1 = 0
 
 glitch_data = Writer(
@@ -45,7 +45,7 @@ print data.predict_fstat()
 
 dtglitch = [duration/4.0, 4*duration/5.0]
 delta_phi = [0, 0]
-delta_F0 = [0.4e-5, 0.3e-6]
+delta_F0 = [4e-6, 3e-7]
 delta_F1 = [0, 0]
 delta_F2 = [0, 0]