diff --git a/examples/natmod/uzlib/Makefile b/examples/natmod/heapq/Makefile
similarity index 68%
rename from examples/natmod/uzlib/Makefile
rename to examples/natmod/heapq/Makefile
index 8761caf2dd26..af45b472da1a 100644
--- a/examples/natmod/uzlib/Makefile
+++ b/examples/natmod/heapq/Makefile
@@ -1,11 +1,11 @@
 # Location of top-level MicroPython directory
 MPY_DIR = ../../..
 
-# Name of module (different to built-in uzlib so it can coexist)
-MOD = uzlib_$(ARCH)
+# Name of module (different to built-in heapq so it can coexist)
+MOD = heapq_$(ARCH)
 
 # Source files (.c or .py)
-SRC = uzlib.c
+SRC = heapq.c
 
 # Architecture to build for (x86, x64, armv7m, xtensa, xtensawin)
 ARCH = x64
diff --git a/examples/natmod/uheapq/uheapq.c b/examples/natmod/heapq/heapq.c
similarity index 100%
rename from examples/natmod/uheapq/uheapq.c
rename to examples/natmod/heapq/heapq.c
diff --git a/examples/natmod/uheapq/Makefile b/examples/natmod/random/Makefile
similarity index 67%
rename from examples/natmod/uheapq/Makefile
rename to examples/natmod/random/Makefile
index 55de3cc08185..5c50227b15f9 100644
--- a/examples/natmod/uheapq/Makefile
+++ b/examples/natmod/random/Makefile
@@ -1,11 +1,11 @@
 # Location of top-level MicroPython directory
 MPY_DIR = ../../..
 
-# Name of module (different to built-in uheapq so it can coexist)
-MOD = uheapq_$(ARCH)
+# Name of module (different to built-in random so it can coexist)
+MOD = random_$(ARCH)
 
 # Source files (.c or .py)
-SRC = uheapq.c
+SRC = random.c
 
 # Architecture to build for (x86, x64, armv7m, xtensa, xtensawin)
 ARCH = x64
diff --git a/examples/natmod/urandom/urandom.c b/examples/natmod/random/random.c
similarity index 100%
rename from examples/natmod/urandom/urandom.c
rename to examples/natmod/random/random.c
diff --git a/examples/natmod/ure/Makefile b/examples/natmod/re/Makefile
similarity index 69%
rename from examples/natmod/ure/Makefile
rename to examples/natmod/re/Makefile
index f5254298fdd9..1ba540110650 100644
--- a/examples/natmod/ure/Makefile
+++ b/examples/natmod/re/Makefile
@@ -1,11 +1,11 @@
 # Location of top-level MicroPython directory
 MPY_DIR = ../../..
 
-# Name of module (different to built-in ure so it can coexist)
-MOD = ure_$(ARCH)
+# Name of module (different to built-in re so it can coexist)
+MOD = re_$(ARCH)
 
 # Source files (.c or .py)
-SRC = ure.c
+SRC = re.c
 
 # Architecture to build for (x86, x64, armv7m, xtensa, xtensawin)
 ARCH = x64
diff --git a/examples/natmod/ure/ure.c b/examples/natmod/re/re.c
similarity index 100%
rename from examples/natmod/ure/ure.c
rename to examples/natmod/re/re.c
diff --git a/examples/natmod/urandom/Makefile b/examples/natmod/zlib/Makefile
similarity index 66%
rename from examples/natmod/urandom/Makefile
rename to examples/natmod/zlib/Makefile
index 3f018baaf76b..e4b4e0712ef2 100644
--- a/examples/natmod/urandom/Makefile
+++ b/examples/natmod/zlib/Makefile
@@ -1,11 +1,11 @@
 # Location of top-level MicroPython directory
 MPY_DIR = ../../..
 
-# Name of module (different to built-in urandom so it can coexist)
-MOD = urandom_$(ARCH)
+# Name of module (different to built-in zlib so it can coexist)
+MOD = zlib_$(ARCH)
 
 # Source files (.c or .py)
-SRC = urandom.c
+SRC = zlib.c
 
 # Architecture to build for (x86, x64, armv7m, xtensa, xtensawin)
 ARCH = x64
diff --git a/examples/natmod/uzlib/uzlib.c b/examples/natmod/zlib/zlib.c
similarity index 100%
rename from examples/natmod/uzlib/uzlib.c
rename to examples/natmod/zlib/zlib.c
diff --git a/tools/ci.sh b/tools/ci.sh
index 8d361e2b3972..21acc17535bb 100755
--- a/tools/ci.sh
+++ b/tools/ci.sh
@@ -454,10 +454,10 @@ function ci_native_mpy_modules_build {
     make -C examples/natmod/features3 ARCH=$arch
     make -C examples/natmod/btree ARCH=$arch
     make -C examples/natmod/framebuf ARCH=$arch
-    make -C examples/natmod/uheapq ARCH=$arch
-    make -C examples/natmod/urandom ARCH=$arch
-    make -C examples/natmod/ure ARCH=$arch
-    make -C examples/natmod/uzlib ARCH=$arch
+    make -C examples/natmod/heapq ARCH=$arch
+    make -C examples/natmod/random ARCH=$arch
+    make -C examples/natmod/re ARCH=$arch
+    make -C examples/natmod/zlib ARCH=$arch
 }
 
 function ci_native_mpy_modules_32bit_build {
@@ -523,7 +523,7 @@ function ci_unix_coverage_run_mpy_merge_tests {
 
 function ci_unix_coverage_run_native_mpy_tests {
     MICROPYPATH=examples/natmod/features2 ./ports/unix/build-coverage/micropython -m features2
-    (cd tests && ./run-natmodtests.py "$@" extmod/{btree*,framebuf*,uheapq*,urandom*,ure*,uzlib*}.py)
+    (cd tests && ./run-natmodtests.py "$@" extmod/{btree*,framebuf*,heapq*,random*,re*,zlib*}.py)
 }
 
 function ci_unix_32bit_setup {