diff --git a/Mmake.common.in b/Mmake.common.in
index db455710a..7523a7ea1 100644
--- a/Mmake.common.in
+++ b/Mmake.common.in
@@ -291,8 +291,8 @@ NM 			= @NM@
 # The inclusion of Mmake.workspace.
 #
 # We should swap the sections that include Mmake.workspace and Mmake.params,
-# as this should allow the instructions in README.java.md and README.CSharp.md
-# to be simplified.
+# as this should allow the instructions in Documentation/README.Java.md and
+# Documentation/README.CSharp.md to be simplified.
 #
 
 # The rpath for the libraries needs to be set to the final installation
diff --git a/RELEASE_NOTES b/RELEASE_NOTES
index be990831e..745d7821b 100644
--- a/RELEASE_NOTES
+++ b/RELEASE_NOTES
@@ -141,7 +141,8 @@ significantly better than all previous Prolog systems known to us.  However,
 the system does not need these extensions, and will work in their absence.
 
 The Mercury compiler can also compile Mercury programs to Java or C#.
-See README.Java.md and README.CSharp.md respectively.
+See Documentation/README.Java.md and Documentation/README.CSharp.md
+respectively.
 
 The current Mercury system has been tested on Linux (x86, x86_64, arm),
 macOS (x86_64), Windows 7 and Windows 10 (x86 and x86_64),
@@ -162,7 +163,8 @@ later.  Do not use gcc versions 2.96, 3.0 or 4.0; those versions have bugs that
 cause trouble for Mercury.  If you are using gcc, you will need at least
 version 2.95 or higher, except on Mac OS X where you will need version 3.3 or
 higher.  Visual C++ or clang may also be used as a C compiler.
-(See README.MS-VisualC.md and README.clang.md for further details.)
+(See Documentation/README.MS-VisualC.md and Documentation/README.clang.md for
+further details.)
 You will also need GNU make version 3.69 or higher.
 
 The Mercury distribution contains:
diff --git a/configure.ac b/configure.ac
index 1489232be..7330133ac 100644
--- a/configure.ac
+++ b/configure.ac
@@ -276,7 +276,7 @@ then
 [
 **** Note that this version of Xcode 11 has bugs that prevent Mercury programs
 **** from working correctly.  Please use Xcode 11.4 or later.
-**** See README.MacOS for further details.])
+**** See Documentation/README.macOS.md for further details.])
             ;;
             esac }
          ;;
@@ -4529,7 +4529,8 @@ case "$mercury_cv_cc_type" in
         # Suppress the MSVC banner message.
         CFLAGS_FOR_WARNINGS="-nologo"
         CFLAGS_FOR_OPT=
-        # XXX See README.MS-Visual C for details of why we disable this.
+        # XXX See Documentation/README.MS-VisualC.md for details of why we
+        # disable this.
         #CFLAGS_FOR_DEBUG="-Zi"
         CFLAGS_FOR_DEBUG=
         CFLAGS_FOR_NO_STRICT_ALIASING=
diff --git a/scripts/mgnuc.in b/scripts/mgnuc.in
index 4b83a6527..f60c90f37 100644
--- a/scripts/mgnuc.in
+++ b/scripts/mgnuc.in
@@ -83,7 +83,8 @@ case "${C_COMPILER_TYPE}" in
     msvc*)
         CHECK_OPTS="-nologo"    # Suppress the MSVC banner message.
         OPT_OPTS="-O1"
-        # See README.MS-VisualC for why we don't enable C level debugging.
+        # See Documentation/README.MS-VisualC.md for why we don't enable C
+        # level debugging.
         #DEBUG_OPTS="-Zi"
         DEBUG_OPTS=""
         DISABLE_OPTS_OPT="-Od"
diff --git a/tools/bootcheck b/tools/bootcheck
index 832c865e6..3c78b8177 100755
--- a/tools/bootcheck
+++ b/tools/bootcheck
@@ -1206,8 +1206,8 @@ then
         # For the csharp grade, Mmake.workspace needs to see the grade setting
         # when it defines MLLIBS, otherwise we will try to reference a separate
         # Mercury runtime assembly, which we do not have for the csharp grade.
-        # As per README.Csharp, we need to set GRADE as part of the command
-        # line that invokes mmake.
+        # As per Documentation/README.CSharp.md, we need to set GRADE as part
+        # of the command line that invokes mmake.
         if test "${grade}" = "csharp"
         then
             ENVGRADE="GRADE=${grade}"
diff --git a/tools/configure_cross b/tools/configure_cross
index 50d20d193..793a0428f 100755
--- a/tools/configure_cross
+++ b/tools/configure_cross
@@ -8,7 +8,7 @@
 #---------------------------------------------------------------------------#
 #
 # This script prepares the Mercury source tree for building with a
-# C cross-compiler. Please see README.cross.md for details.
+# C cross-compiler. Please see Documentation/README.cross.md for details.
 #
 #---------------------------------------------------------------------------#
 
diff --git a/tools/copy_mercury_binaries b/tools/copy_mercury_binaries
index 9e2adeaee..3283b0c13 100755
--- a/tools/copy_mercury_binaries
+++ b/tools/copy_mercury_binaries
@@ -7,7 +7,7 @@
 #---------------------------------------------------------------------------#
 #
 # This script copies the binaries from one Mercury installation to another.
-# Please see README.cross.md for details.
+# Please see Documentation/README.cross.md for details.
 #
 #---------------------------------------------------------------------------#