diff --git a/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/CliFormatterCursor.java b/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/CliFormatterCursor.java
index e5002e6e1e9..974eed339ea 100644
--- a/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/CliFormatterCursor.java
+++ b/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/CliFormatterCursor.java
@@ -22,9 +22,13 @@ import java.util.Objects;
 public class CliFormatterCursor implements Cursor {
     public static final String NAME = "f";
 
-    private Cursor delegate;
-    private CliFormatter formatter;
+    private final Cursor delegate;
+    private final CliFormatter formatter;
 
+    /**
+     * If the newCursor is empty, returns an empty cursor. Otherwise, creates a new
+     * CliFormatterCursor that wraps the newCursor.
+     */
     public static Cursor wrap(Cursor newCursor, CliFormatter formatter) {
         if (newCursor == EMPTY) {
             return EMPTY;
@@ -32,7 +36,7 @@ public class CliFormatterCursor implements Cursor {
         return new CliFormatterCursor(newCursor, formatter);
     }
 
-    public CliFormatterCursor(Cursor delegate, CliFormatter formatter) {
+    private CliFormatterCursor(Cursor delegate, CliFormatter formatter) {
         this.delegate = delegate;
         this.formatter = formatter;
     }
diff --git a/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/JdbcCursor.java b/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/JdbcCursor.java
index 31aefdaf939..f7cbadb2588 100644
--- a/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/JdbcCursor.java
+++ b/sql/server/src/main/java/org/elasticsearch/xpack/sql/plugin/JdbcCursor.java
@@ -24,10 +24,13 @@ import java.util.Objects;
  */
 public class JdbcCursor implements Cursor {
     public static final String NAME = "j";
-    private Cursor delegate;
-    private List<JDBCType> types;
-
+    private final Cursor delegate;
+    private final List<JDBCType> types;
 
+    /**
+     * If the newCursor is empty, returns an empty cursor. Otherwise, creates a new
+     * CliFormatterCursor that wraps the newCursor.
+     */
     public static Cursor wrap(Cursor newCursor, List<JDBCType> types) {
         if (newCursor == EMPTY) {
             return EMPTY;
@@ -35,7 +38,7 @@ public class JdbcCursor implements Cursor {
         return new JdbcCursor(newCursor, types);
     }
 
-    public JdbcCursor(Cursor delegate, List<JDBCType> types) {
+    private JdbcCursor(Cursor delegate, List<JDBCType> types) {
         this.delegate = delegate;
         this.types = types;
     }
diff --git a/sql/server/src/test/java/org/elasticsearch/xpack/sql/plugin/sql/action/SqlResponseTests.java b/sql/server/src/test/java/org/elasticsearch/xpack/sql/plugin/sql/action/SqlResponseTests.java
index a9da155e646..bb51f5d5df0 100644
--- a/sql/server/src/test/java/org/elasticsearch/xpack/sql/plugin/sql/action/SqlResponseTests.java
+++ b/sql/server/src/test/java/org/elasticsearch/xpack/sql/plugin/sql/action/SqlResponseTests.java
@@ -44,11 +44,11 @@ public class SqlResponseTests extends AbstractStreamableTestCase<SqlResponse> {
                 for (int i = 0; i < typeNum; i++) {
                     types.add(randomFrom(JDBCType.values()));
                 }
-                return new JdbcCursor(ScrollCursorTests.randomScrollCursor(), types);
+                return JdbcCursor.wrap(ScrollCursorTests.randomScrollCursor(), types);
             case 2:
                 SqlResponse response = createRandomInstance(Cursor.EMPTY);
                 if (response.columns() != null && response.rows() != null) {
-                    return new CliFormatterCursor(ScrollCursorTests.randomScrollCursor(), new CliFormatter(response));
+                    return CliFormatterCursor.wrap(ScrollCursorTests.randomScrollCursor(), new CliFormatter(response));
                 } else {
                     return ScrollCursorTests.randomScrollCursor();
                 }