diff --git a/cronic b/cronic
index b26d786..3c92872 100755
--- a/cronic
+++ b/cronic
@@ -15,6 +15,21 @@
 # The options and the treatment of execution traces are documented in function
 # `cronic_help`; run `cronic --help`.
 
+# The caller's options, as commands that restore them.  This script restores
+# the caller's options while it runs the wrapped command.  Otherwise, any bash
+# script that the wrapped command runs, such as a `#!/bin/bash` script, would
+# get this script's `set -eu` rather than the caller's options and, for example,
+# fail on its first unset variable.
+# Limitation:  if the wrapped command is a builtin that runs code in this
+# script's shell, such as `source` or `eval`, that code also runs with the
+# caller's options, even if the caller does not export SHELLOPTS.  So if the
+# caller does not use `set -u`, that code silently expands an unset variable
+# to the empty string.
+# Not `$(set +o)`, because a command substitution, unlike a process
+# substitution, does not inherit `set -e`.  `read` exits with status 1 at the
+# end of its input.
+read -r -d '' cronic_caller_opts < <(set +o) || true
+
 # Exit if a command exits with a non-zero status, and treat unset variables
 # as an error.
 set -eu
@@ -158,11 +173,17 @@ if ((BASH_VERSINFO[0] > 4 || (BASH_VERSINFO[0] == 4 && BASH_VERSINFO[1] >= 1)));
   export BASH_XTRACEFD=$cronic_xtrace_fd
 fi
 
+# The wrapped command runs in a subshell with the caller's options.  It is not
+# the operand of `||` or the like, because then bash would ignore `set -e` and
+# would remove "errexit" from the SHELLOPTS that the wrapped command inherits.
 set +e
-# `command` because the wrapped command runs in this shell, where a function of
-# this script, such as `cronic_usage`, would otherwise run in place of a
-# program of the same name.
-command -- "$@" > "$cronic_out" 2> "$cronic_trace"
+(
+  eval "$cronic_caller_opts"
+  # `command` because the wrapped command runs in a subshell of this shell,
+  # where a function of this script, such as `cronic_usage`, would otherwise
+  # run in place of a program of the same name.
+  command -- "$@"
+) > "$cronic_out" 2> "$cronic_trace"
 cronic_result=$?
 set -e
 
diff --git a/tests/cronic-test/cronic-test.sh b/tests/cronic-test/cronic-test.sh
index 7b62509..dcd1a9b 100755
--- a/tests/cronic-test/cronic-test.sh
+++ b/tests/cronic-test/cronic-test.sh
@@ -374,4 +374,30 @@ check "PS4 with a newline, error line that contains its second line" 0 \
   "report:^error: bad b input$" "$work/stderr-lines" "error: bad b input"
 unset PS4
 
+# A command that expands an unset variable.
+cat > "$work/unset-variable" << 'EOF'
+#!/bin/bash
+echo "${cronic_test_unset_variable}"
+EOF
+chmod +x "$work/unset-variable"
+
+# A caller that sets the option given as its first argument, such as `-u` or
+# `+u`, and exports SHELLOPTS.  When the caller exports SHELLOPTS, the wrapped
+# command gets the caller's `set -u` setting, not `cronic`'s.
+cat > "$work/caller" << EOF
+#!/bin/bash
+set "\$1"
+shift
+export SHELLOPTS
+exec "$CRONIC" "\$@"
+EOF
+chmod +x "$work/caller"
+saved_cronic="$CRONIC"
+CRONIC="$work/caller"
+check "exported SHELLOPTS without nounset, unset variable" 0 silent \
+  +u "$work/unset-variable"
+check "exported SHELLOPTS with nounset, unset variable" 1 \
+  "report:unbound variable" -u "$work/unset-variable"
+CRONIC="$saved_cronic"
+
 exit "$status"