diff --git a/doc/src/sgml/ref/copy.sgml b/doc/src/sgml/ref/copy.sgml
index 40af423ccf1..8aae711b3b9 100644
--- a/doc/src/sgml/ref/copy.sgml
+++ b/doc/src/sgml/ref/copy.sgml
@@ -282,6 +282,8 @@ COPY { <replaceable class="parameter">table_name</replaceable> [ ( <replaceable
       of the columns in the header line must match the actual column names of
       the table, otherwise an error is raised.
       This option is not allowed when using <literal>binary</literal> format.
+      The <literal>MATCH</literal> option is only valid for <command>COPY
+      FROM</command> commands.
      </para>
     </listitem>
    </varlistentry>
diff --git a/src/backend/commands/copy.c b/src/backend/commands/copy.c
index f448d39c7ed..e2870e3c11c 100644
--- a/src/backend/commands/copy.c
+++ b/src/backend/commands/copy.c
@@ -318,7 +318,7 @@ DoCopy(ParseState *pstate, const CopyStmt *stmt,
  * defGetBoolean() but also accepts the special value "match".
  */
 static CopyHeaderChoice
-defGetCopyHeaderChoice(DefElem *def)
+defGetCopyHeaderChoice(DefElem *def, bool is_from)
 {
 	/*
 	 * If no parameter given, assume "true" is meant.
@@ -360,7 +360,14 @@ defGetCopyHeaderChoice(DefElem *def)
 				if (pg_strcasecmp(sval, "off") == 0)
 					return COPY_HEADER_FALSE;
 				if (pg_strcasecmp(sval, "match") == 0)
+				{
+					if (!is_from)
+						ereport(ERROR,
+								(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+								 errmsg("cannot use \"%s\" with HEADER in COPY TO",
+										sval)));
 					return COPY_HEADER_MATCH;
+				}
 			}
 			break;
 	}
@@ -452,7 +459,7 @@ ProcessCopyOptions(ParseState *pstate,
 			if (header_specified)
 				errorConflictingDefElem(defel, pstate);
 			header_specified = true;
-			opts_out->header_line = defGetCopyHeaderChoice(defel);
+			opts_out->header_line = defGetCopyHeaderChoice(defel, is_from);
 		}
 		else if (strcmp(defel->defname, "quote") == 0)
 		{
diff --git a/src/backend/commands/copyfromparse.c b/src/backend/commands/copyfromparse.c
index e06534943f7..57813b3458b 100644
--- a/src/backend/commands/copyfromparse.c
+++ b/src/backend/commands/copyfromparse.c
@@ -789,11 +789,12 @@ NextCopyFromRawFields(CopyFromState cstate, char ***fields, int *nfields)
 			foreach(cur, cstate->attnumlist)
 			{
 				int			attnum = lfirst_int(cur);
-				char	   *colName = cstate->raw_fields[attnum - 1];
+				char	   *colName;
 				Form_pg_attribute attr = TupleDescAttr(tupDesc, attnum - 1);
 
-				fldnum++;
+				Assert(fldnum < cstate->max_fields);
 
+				colName = cstate->raw_fields[fldnum++];
 				if (colName == NULL)
 					ereport(ERROR,
 							(errcode(ERRCODE_BAD_COPY_FILE_FORMAT),
diff --git a/src/test/regress/expected/copy.out b/src/test/regress/expected/copy.out
index e8d6b4fc13b..7f2f4ae4aea 100644
--- a/src/test/regress/expected/copy.out
+++ b/src/test/regress/expected/copy.out
@@ -182,9 +182,21 @@ create table header_copytest (
 	b int,
 	c text
 );
+-- Make sure it works with with dropped columns
+alter table header_copytest drop column c;
+alter table header_copytest add column c text;
+copy header_copytest to stdout with (header match);
+ERROR:  cannot use "match" with HEADER in COPY TO
 copy header_copytest from stdin with (header wrong_choice);
 ERROR:  header requires a Boolean value or "match"
+-- works
 copy header_copytest from stdin with (header match);
+copy header_copytest (c, a, b) from stdin with (header match);
+copy header_copytest from stdin with (header match, format csv);
+-- errors
+copy header_copytest (c, b, a) from stdin with (header match);
+ERROR:  column name mismatch in header line field 1: got "a", expected "c"
+CONTEXT:  COPY header_copytest, line 1: "a	b	c"
 copy header_copytest from stdin with (header match);
 ERROR:  column name mismatch in header line field 3: got null value ("\N"), expected "c"
 CONTEXT:  COPY header_copytest, line 1: "a	b	\N"
@@ -197,5 +209,34 @@ CONTEXT:  COPY header_copytest, line 1: "a	b	c	d"
 copy header_copytest from stdin with (header match);
 ERROR:  column name mismatch in header line field 3: got "d", expected "c"
 CONTEXT:  COPY header_copytest, line 1: "a	b	d"
-copy header_copytest from stdin with (header match, format csv);
+SELECT * FROM header_copytest ORDER BY a;
+ a | b |  c  
+---+---+-----
+ 1 | 2 | foo
+ 3 | 4 | bar
+ 5 | 6 | baz
+(3 rows)
+
+-- Drop an extra column, in the middle of the existing set.
+alter table header_copytest drop column b;
+-- works
+copy header_copytest (c, a) from stdin with (header match);
+copy header_copytest (a, c) from stdin with (header match);
+-- errors
+copy header_copytest from stdin with (header match);
+ERROR:  wrong number of fields in header line: field count is 3, expected 2
+CONTEXT:  COPY header_copytest, line 1: "a	........pg.dropped.2........	c"
+copy header_copytest (a, c) from stdin with (header match);
+ERROR:  wrong number of fields in header line: field count is 3, expected 2
+CONTEXT:  COPY header_copytest, line 1: "a	c	b"
+SELECT * FROM header_copytest ORDER BY a;
+ a |  c  
+---+-----
+ 1 | foo
+ 3 | bar
+ 5 | baz
+ 7 | foo
+ 8 | foo
+(5 rows)
+
 drop table header_copytest;
diff --git a/src/test/regress/sql/copy.sql b/src/test/regress/sql/copy.sql
index d72d226f341..285022e07c6 100644
--- a/src/test/regress/sql/copy.sql
+++ b/src/test/regress/sql/copy.sql
@@ -204,11 +204,29 @@ create table header_copytest (
 	b int,
 	c text
 );
+-- Make sure it works with with dropped columns
+alter table header_copytest drop column c;
+alter table header_copytest add column c text;
+copy header_copytest to stdout with (header match);
 copy header_copytest from stdin with (header wrong_choice);
+-- works
 copy header_copytest from stdin with (header match);
 a	b	c
 1	2	foo
 \.
+copy header_copytest (c, a, b) from stdin with (header match);
+c	a	b
+bar	3	4
+\.
+copy header_copytest from stdin with (header match, format csv);
+a,b,c
+5,6,baz
+\.
+-- errors
+copy header_copytest (c, b, a) from stdin with (header match);
+a	b	c
+1	2	foo
+\.
 copy header_copytest from stdin with (header match);
 a	b	\N
 1	2	foo
@@ -225,8 +243,28 @@ copy header_copytest from stdin with (header match);
 a	b	d
 1	2	foo
 \.
-copy header_copytest from stdin with (header match, format csv);
-a,b,c
-1,2,foo
+SELECT * FROM header_copytest ORDER BY a;
+
+-- Drop an extra column, in the middle of the existing set.
+alter table header_copytest drop column b;
+-- works
+copy header_copytest (c, a) from stdin with (header match);
+c	a
+foo	7
 \.
+copy header_copytest (a, c) from stdin with (header match);
+a	c
+8	foo
+\.
+-- errors
+copy header_copytest from stdin with (header match);
+a	........pg.dropped.2........	c
+1	2	foo
+\.
+copy header_copytest (a, c) from stdin with (header match);
+a	c	b
+1	foo	2
+\.
+
+SELECT * FROM header_copytest ORDER BY a;
 drop table header_copytest;