diff --git a/tests/invalid-elf.sh b/tests/invalid-elf.sh
index cc8577c2..7145c793 100755
--- a/tests/invalid-elf.sh
+++ b/tests/invalid-elf.sh
@@ -21,6 +21,67 @@ TEST_CASES="invalid-shrstrtab-idx invalid-shrstrtab-size invalid-shrstrtab-zero
 # Issue #64 regression test. Test ELF provided by issue submitter.
 TEST_CASES=$TEST_CASES' invalid-phdr-issue-64'
 
+# Issue #132 regression test. Test ELF provided by issue submitter.
+TEST_CASES=$TEST_CASES' invalid-shrink-rpath-issue-132'
+
+# Issue #133 regression test. Test ELFs provided by issue submitter.
+set -x
+for i in $(seq 0 5); do
+    # Not yet fixed!
+    if [ "$i" = 3 ]; then continue; fi
+    TEST_CASES=$TEST_CASES' invalid-strlen-issue-133-'$i
+done
+set +x
+
+# Issue #134 regression test. Test ELFs provided by issue submitter.
+set -x
+for i in $(seq 0 1); do
+    TEST_CASES=$TEST_CASES' invalid-null-ptr-issue-134-'$i
+done
+set +x
+
+# Not yet fixed!
+# Issue #132 regression test. Test ELF provided by issue submitter.
+#TEST_CASES=$TEST_CASES' invalid-string-index-issue-135'
+
+# Some ELFs are immediately recognized as invalid. Others, we need to
+# attempt an operation to notice the problem.
+
+# shellcheck disable=SC2034
+invalid_shrstrtab_idx_CMDS=''
+# shellcheck disable=SC2034
+invalid_shrstrtab_size_CMDS=''
+# shellcheck disable=SC2034
+invalid_shrstrtab_zero_CMDS=''
+# shellcheck disable=SC2034
+invalid_shrstrtab_nonterm_CMDS=''
+# shellcheck disable=SC2034
+invalid_shdr_name_CMDS=''
+# shellcheck disable=SC2034
+invalid_phdr_offset_CMDS=''
+# shellcheck disable=SC2034
+invalid_phdr_issue_64_CMDS=''
+# shellcheck disable=SC2034
+invalid_shrink_rpath_issue_132_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_0_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_1_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_2_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_3_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_4_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_5_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_null_ptr_issue_134_0_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_null_ptr_issue_134_1_CMDS='--shrink-rpath'
+# shellcheck disable=SC2034
+invalid_string_index_issue_135_CMDS='--shrink-rpath'
+
 # shellcheck disable=SC2034
 invalid_shrstrtab_idx_MSG='data region extends past file end'
 # shellcheck disable=SC2034
@@ -35,24 +96,53 @@ invalid_shdr_name_MSG='data region extends past file end'
 invalid_phdr_offset_MSG='data region extends past file end'
 # shellcheck disable=SC2034
 invalid_phdr_issue_64_MSG='program header table out of bounds'
+# shellcheck disable=SC2034
+invalid_shrink_rpath_issue_132_MSG='data region extends past file end'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_0_MSG='section name offset out of bounds'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_1_MSG='data region extends past file end'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_2_MSG='string table is not zero terminated'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_3_MSG='not sure yet'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_4_MSG='data region extends past file end'
+# shellcheck disable=SC2034
+invalid_strlen_issue_133_5_MSG='string table size is zero'
+# shellcheck disable=SC2034
+invalid_null_ptr_issue_134_0_MSG='no section headers'
+# shellcheck disable=SC2034
+invalid_null_ptr_issue_134_1_MSG='no section headers'
+# shellcheck disable=SC2034
+invalid_string_index_issue_135_MSG='no sure yet'
 
 FAILED_TESTS=""
 
 for tcase in $TEST_CASES; do
     if [ ! -r "$TEST_DIR/$tcase" ]; then
-	echo "Cannot read test case: $tcase"
-	exit 1
+    echo "Cannot read test case: $tcase"
+    exit 1
     fi
 
-    ../src/patchelf --output /dev/null "$TEST_DIR/$tcase" && res=$? || res=$?
+    var=$(echo "$tcase-CMDS" | tr '-' '_')
+    cmds=
+    eval "cmds=\${$var}"
+
+    # Want the word-splitting, no arrays in POSIX shell
+    # shellcheck disable=SC2086
+    ../src/patchelf $cmds --output /dev/null "$TEST_DIR/$tcase" && res=$? || res=$?
     if killed_by_signal "$res"; then
-	FAILED_TESTS="$FAILED_TESTS $tcase"
+    FAILED_TESTS="$FAILED_TESTS $tcase"
     fi
 
     var=$(echo "$tcase-MSG" | tr '-' '_')
     msg=
     eval "msg=\${$var}"
-    ../src/patchelf --output /dev/null "$TEST_DIR/$tcase" 2>&1 |
+
+    # Want the word-splitting, no arrays in POSIX shell
+    # shellcheck disable=SC2086
+    ../src/patchelf $cmds --output /dev/null "$TEST_DIR/$tcase" 2>&1 |
         grep "$msg" >/dev/null 2>/dev/null
 done
 
diff --git a/tests/invalid-elf/invalid-null-ptr-issue-134-0 b/tests/invalid-elf/invalid-null-ptr-issue-134-0
new file mode 100644
index 00000000..3c2cd178
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diff --git a/tests/invalid-elf/invalid-null-ptr-issue-134-1 b/tests/invalid-elf/invalid-null-ptr-issue-134-1
new file mode 100644
index 00000000..26d5c24c
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diff --git a/tests/invalid-elf/invalid-shrink-rpath-issue-132 b/tests/invalid-elf/invalid-shrink-rpath-issue-132
new file mode 100644
index 00000000..0e8b3fa9
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diff --git a/tests/invalid-elf/invalid-string-index-issue-135 b/tests/invalid-elf/invalid-string-index-issue-135
new file mode 100644
index 00000000..6398ba9c
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-0 b/tests/invalid-elf/invalid-strlen-issue-133-0
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-1 b/tests/invalid-elf/invalid-strlen-issue-133-1
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-2 b/tests/invalid-elf/invalid-strlen-issue-133-2
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-3 b/tests/invalid-elf/invalid-strlen-issue-133-3
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-4 b/tests/invalid-elf/invalid-strlen-issue-133-4
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diff --git a/tests/invalid-elf/invalid-strlen-issue-133-5 b/tests/invalid-elf/invalid-strlen-issue-133-5
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