diff --git a/Exec/gravity_tests/hse_convergence/README.md b/Exec/gravity_tests/hse_convergence/README.md
index fa639f4708..fab88d7bd7 100644
--- a/Exec/gravity_tests/hse_convergence/README.md
+++ b/Exec/gravity_tests/hse_convergence/README.md
@@ -7,29 +7,34 @@ in the plotfiles.
 
 To run this problem, use one of the convergence scripts:
 
-  * ``convergence_plm.sh`` :
+  * `convergence_plm.sh` :
 
-    this runs CTU + PLM using the default HSE BCs and default
-    use_pslope, then with reflect BCs, then without use_pslope, and
-    finally runs with reflect instead of HSE BCs.
+    this runs CTU + PLM using:
+    1. the default HSE BCs and `use_pslope`
+    2. the HSE BCs with reflection and `use_pslope`
+    3. reflect BCs instead of HSE BCs without `use_pslope`
+    4. reflect BCs with `use_pslope`
 
-    These tests show that the best results come from HSE BCs + reflect vel
+    These tests show that the best results (by far) come from
+    `use_pslope=1` and reflecting BCs
 
   * convergence_ppm.sh :
 
     this runs CTU + PPM in a similar set of configurations as PLM above
-    (with one additional one: grav_source_type = 4)
+    1. the default HSE BCs
+    2. HSE BCs with reflection
+    3. reflecting BCs
+    4. reflecting BCs with `use_pslope`
 
-    These tests show that the best results come from HSE BCs + reflect vel
+    These tests show that the best results (by far) come from
+    reflecting BCs with `use_pslope=1`, just like the PLM case.
 
   * convergence_sdc.sh :
 
-    this uses the TRUE_SDC integration, first with SDC-2 + PLM  and reflecting BCs,
-    the SDC-2 + PPM and reflecting BCs, then the same but HSE BCs, and finally
-    SDC-4 + reflect
+    this uses the TRUE_SDC integration, first with SDC-2 + PLM and
+    reflecting BCs, the SDC-2 + PPM and reflecting BCs, then the same
+    but HSE BCs, and finally SDC-4 + reflect
 
     These tests show that the PLM + reflect (which uses the
     well-balanced use_pslope) and the SDC-4 + reflect give the lowest
-    errors and expected (or better) convergence:
-
-
+    errors and expected (or better) convergence.
diff --git a/Exec/gravity_tests/hse_convergence/convergence_plm.sh b/Exec/gravity_tests/hse_convergence/convergence_plm.sh
index 285cfed67d..3d12427ad5 100755
--- a/Exec/gravity_tests/hse_convergence/convergence_plm.sh
+++ b/Exec/gravity_tests/hse_convergence/convergence_plm.sh
@@ -58,43 +58,15 @@ pfile=`ls -t | grep -i hse_512_plt | head -1`
 fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
 
 
-## plm + hse reflect + no pslope
-
-ofile=plm-hsereflect-nopslope.converge.out
-
-RUNPARAMS="
-castro.ppm_type=0
-castro.use_pslope=0
-castro.hse_interp_temp=1
-castro.hse_reflect_vels=1
-"""
-
-${EXEC} inputs.ppm.64 ${RUNPARAMS} >& 64.out
-pfile=`ls -t | grep -i hse_64_plt | head -1`
-fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel > ${ofile}
-
-${EXEC} inputs.ppm.128 ${RUNPARAMS} >& 128.out
-pfile=`ls -t | grep -i hse_128_plt | head -1`
-fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
-
-${EXEC} inputs.ppm.256 ${RUNPARAMS} >& 256.out
-pfile=`ls -t | grep -i hse_256_plt | head -1`
-fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
-
-${EXEC} inputs.ppm.512 ${RUNPARAMS} >& 512.out
-pfile=`ls -t | grep -i hse_512_plt | head -1`
-fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
-
-
-## plm + reflect
+## plm + reflect + nopslope
 
-ofile=plm-reflect.converge.out
+ofile=plm-reflect-nopslope.converge.out
 
 RUNPARAMS="
 castro.ppm_type=0
-castro.use_pslope=1
 castro.lo_bc=3
 castro.hi_bc=3
+castro.use_pslope=0
 """
 
 ${EXEC} inputs.ppm.64 ${RUNPARAMS} >& 64.out
@@ -114,16 +86,15 @@ pfile=`ls -t | grep -i hse_512_plt | head -1`
 fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
 
 
+## plm + reflect + pslope
 
-## plm + reflect + nopslope
-
-ofile=plm-reflect-nopslope.converge.out
+ofile=plm-reflect-pslope.converge.out
 
 RUNPARAMS="
 castro.ppm_type=0
 castro.lo_bc=3
 castro.hi_bc=3
-castro.use_pslope=0
+castro.use_pslope=1
 """
 
 ${EXEC} inputs.ppm.64 ${RUNPARAMS} >& 64.out
diff --git a/Exec/gravity_tests/hse_convergence/convergence_ppm.sh b/Exec/gravity_tests/hse_convergence/convergence_ppm.sh
index ff6e2c7620..27b4bb86ef 100755
--- a/Exec/gravity_tests/hse_convergence/convergence_ppm.sh
+++ b/Exec/gravity_tests/hse_convergence/convergence_ppm.sh
@@ -50,12 +50,13 @@ pfile=`ls -t | grep -i hse_512_plt | head -1`
 fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
 
 
-## ppm + grav_source_type = 4
+## ppm + reflect
 
-ofile=ppm-grav4.converge.out
+ofile=ppm-reflect.converge.out
 
 RUNPARAMS="
-castro.grav_source_type=4
+castro.lo_bc=3
+castro.hi_bc=3
 """
 
 ${EXEC} inputs.ppm.64 ${RUNPARAMS} >& 64.out
@@ -75,13 +76,14 @@ pfile=`ls -t | grep -i hse_512_plt | head -1`
 fextrema.gnu.ex -v magvel ${pfile} | grep -i magvel >> ${ofile}
 
 
-## ppm + reflect
+## ppm + reflect + pslope
 
-ofile=ppm-reflect.converge.out
+ofile=ppm-reflect-pslope.converge.out
 
 RUNPARAMS="
 castro.lo_bc=3
 castro.hi_bc=3
+castro.use_pslope=1
 """
 
 ${EXEC} inputs.ppm.64 ${RUNPARAMS} >& 64.out