diff --git a/src/deh_soc.c b/src/deh_soc.c
index 2e11d2ba2..6787b7b2f 100644
--- a/src/deh_soc.c
+++ b/src/deh_soc.c
@@ -1372,13 +1372,6 @@ void readlevelheader(MYFILE *f, char * name)
 				else
 					mapheaderinfo[num]->menuflags &= ~LF2_HIDEINMENU;
 			}
-			else if (fastcmp(word, "HIDEINSTATS"))
-			{
-				if (i || word2[0] == 'T' || word2[0] == 'Y')
-					mapheaderinfo[num]->menuflags |= LF2_HIDEINSTATS;
-				else
-					mapheaderinfo[num]->menuflags &= ~LF2_HIDEINSTATS;
-			}
 			else if (fastcmp(word, "NOTIMEATTACK") || fastcmp(word, "NORECORDATTACK"))
 			{ // RECORDATTACK is an accepted alias
 				if (i || word2[0] == 'T' || word2[0] == 'Y')
@@ -1393,6 +1386,13 @@ void readlevelheader(MYFILE *f, char * name)
 				else
 					mapheaderinfo[num]->menuflags &= ~LF2_FINISHNEEDED;
 			}
+			else if (fastcmp(word, "NOVISITNEEDED"))
+			{
+				if (i || word2[0] == 'T' || word2[0] == 'Y')
+					mapheaderinfo[num]->menuflags |= LF2_NOVISITNEEDED;
+				else
+					mapheaderinfo[num]->menuflags &= ~LF2_NOVISITNEEDED;
+			}
 			else if (fastcmp(word, "GRAVITY"))
 				mapheaderinfo[num]->gravity = FLOAT_TO_FIXED(atof(word2));
 			else if (fastcmp(word, "DESTROYOBJECTSFORCHALLENGES"))
diff --git a/src/deh_tables.c b/src/deh_tables.c
index 135b79456..2682f7d2b 100644
--- a/src/deh_tables.c
+++ b/src/deh_tables.c
@@ -6853,8 +6853,8 @@ struct int_const_s const INT_CONST[] = {
 	{"LF_SUBTRACTNUM",LF_SUBTRACTNUM},
 	// And map flags
 	{"LF2_HIDEINMENU",LF2_HIDEINMENU},
-	{"LF2_HIDEINSTATS",LF2_HIDEINSTATS},
 	{"LF2_NOTIMEATTACK",LF2_NOTIMEATTACK},
+	{"LF2_NOVISITNEEDED",LF2_NOVISITNEEDED},
 	{"LF2_FINISHNEEDED",LF2_FINISHNEEDED},
 
 	// Emeralds
diff --git a/src/doomstat.h b/src/doomstat.h
index 738a3a22e..2839aa313 100644
--- a/src/doomstat.h
+++ b/src/doomstat.h
@@ -572,8 +572,8 @@ struct mapheader_t
 #define LF_SUBTRACTNUM        (1<<3) ///< Use subtractive position number (for bright levels)
 
 #define LF2_HIDEINMENU		(1<<0) ///< Hide in the multiplayer menu
-#define LF2_HIDEINSTATS		(1<<1) ///< Hide in the statistics screen
-#define LF2_NOTIMEATTACK	(1<<2) ///< Hide this map in Time Attack modes
+#define LF2_NOTIMEATTACK	(1<<1) ///< Hide this map in Time Attack modes
+#define LF2_NOVISITNEEDED	(1<<2) ///< Map does not require visitation to be selectable
 #define LF2_FINISHNEEDED	(1<<3) ///< Not available in Time Attack modes until you beat the level
 
 extern mapheader_t** mapheaderinfo;
diff --git a/src/k_menudraw.c b/src/k_menudraw.c
index 96b0b4f98..f0cd65abf 100644
--- a/src/k_menudraw.c
+++ b/src/k_menudraw.c
@@ -205,6 +205,17 @@ void M_PickMenuBGMap(void)
 			continue;
 		}
 
+		if (!(mapheaderinfo[i]->menuflags & LF2_NOVISITNEEDED)
+		&& !(mapheaderinfo[i]->records.mapvisited & MV_VISITED)
+		&& !(
+			mapheaderinfo[i]->cup
+			&& mapheaderinfo[i]->cup->cachedlevels[0] == i
+		))
+		{
+			// Not visited OR head of cup
+			continue;
+		}
+
 		if (M_MapLocked(i + 1) == true)
 		{
 			// We haven't earned this one.
@@ -7177,7 +7188,7 @@ static void M_DrawStatsMaps(void)
 		for (i = 0; i < nummapheaders; i++)
 		{
 			// Check for no visibility
-			if (!mapheaderinfo[i] || (mapheaderinfo[i]->menuflags & (LF2_NOTIMEATTACK|LF2_HIDEINSTATS|LF2_HIDEINMENU)))
+			if (!mapheaderinfo[i] || (mapheaderinfo[i]->menuflags & (LF2_NOTIMEATTACK|LF2_HIDEINMENU)))
 				continue;
 
 			// Has to be accessible via time attack
diff --git a/src/m_cond.c b/src/m_cond.c
index e170f8fe6..d38db3930 100644
--- a/src/m_cond.c
+++ b/src/m_cond.c
@@ -1094,7 +1094,7 @@ static void M_PrecacheLevelLocks(void)
 							{
 								if (!mapheaderinfo[mapcheck] || mapheaderinfo[mapcheck]->cup != NULL)
 									continue;
-								if (mapheaderinfo[mapcheck]->menuflags & (LF2_HIDEINSTATS|LF2_HIDEINMENU))
+								if (mapheaderinfo[mapcheck]->menuflags & LF2_HIDEINMENU)
 									continue;
 								if (((mapheaderinfo[mapcheck]->typeoflevel & TOL_TUTORIAL) == TOL_TUTORIAL)
 									!= ((mapheaderinfo[map]->typeoflevel & TOL_TUTORIAL) == TOL_TUTORIAL))
@@ -1475,7 +1475,7 @@ boolean M_CheckCondition(condition_t *cn, player_t *player)
 			{
 				for (i = 0; i < basenummapheaders; i++)
 				{
-					if (!mapheaderinfo[i] || mapheaderinfo[i]->menuflags & (LF2_HIDEINSTATS|LF2_HIDEINMENU))
+					if (!mapheaderinfo[i] || mapheaderinfo[i]->menuflags & (LF2_HIDEINMENU))
 						continue;
 
 					total++;
@@ -1957,7 +1957,7 @@ static char *M_BuildConditionTitle(UINT16 map)
 {
 	char *title, *ref;
 
-	if (((mapheaderinfo[map]->menuflags & LF2_FINISHNEEDED)
+	if ((!(mapheaderinfo[map]->menuflags & LF2_NOVISITNEEDED)
 	// the following is intentionally not MV_BEATEN, just in case the title is for "Finish a round on X"
 	&& !(mapheaderinfo[map]->records.mapvisited & MV_VISITED))
 	|| M_MapLocked(map+1))
diff --git a/src/menus/extras-statistics.c b/src/menus/extras-statistics.c
index 1c2866c5a..293c90227 100644
--- a/src/menus/extras-statistics.c
+++ b/src/menus/extras-statistics.c
@@ -21,13 +21,22 @@ static boolean M_StatisticsAddMap(UINT16 map, cupheader_t *cup, boolean *headere
 		return false;
 
 	// Check for no visibility
-	if (mapheaderinfo[map]->menuflags & (LF2_HIDEINSTATS|LF2_HIDEINMENU))
+	if (mapheaderinfo[map]->menuflags & LF2_HIDEINMENU)
 		return false;
 
+	// Check for visitation
+	// (M_CanShowLevelInList also checks being the first map in a cup,
+	// but we don't need to do this here because it'd just muddy stats!)
+	if (!(mapheaderinfo[map]->menuflags & LF2_NOVISITNEEDED)
+	&& !(mapheaderinfo[map]->records.mapvisited & MV_VISITED))
+		return false;
+
+#if 0
 	// Check for completion
 	if ((mapheaderinfo[map]->menuflags & LF2_FINISHNEEDED)
 	&& !(mapheaderinfo[map]->records.mapvisited & MV_BEATEN))
 		return false;
+#endif
 
 	// Check for unlock
 	if (M_MapLocked(map+1))
@@ -80,11 +89,7 @@ static void M_StatisticsMaps(void)
 	headerexists = false;
 	for (i = 0; i < nummapheaders; i++)
 	{
-		if (M_StatisticsAddMap(i, NULL, &headerexists, true))
-		{
-			if (!(mapheaderinfo[i]->records.mapvisited & MV_BEATEN))
-				break;
-		}
+		M_StatisticsAddMap(i, NULL, &headerexists, true);
 	}
 
 	if ((i = statisticsmenu.numextramedals) != 0)
diff --git a/src/menus/transient/level-select.c b/src/menus/transient/level-select.c
index 73189a3bb..28eed536a 100644
--- a/src/menus/transient/level-select.c
+++ b/src/menus/transient/level-select.c
@@ -77,11 +77,11 @@ boolean M_CanShowLevelInList(INT16 mapnum, levelsearch_t *levelsearch)
 	if (levelsearch->timeattack && (mapheaderinfo[mapnum]->menuflags & LF2_NOTIMEATTACK))
 		return false;
 
+	cupheader_t *cup = (levelsearch->cup == &dummy_lostandfound) ? NULL : levelsearch->cup;
+
 	// Don't permit cup when no cup requested (also no dupes in time attack)
 	if (levelsearch->cupmode)
 	{
-		cupheader_t *cup = (levelsearch->cup == &dummy_lostandfound) ? NULL : levelsearch->cup;
-
 		if ((!cup || levelsearch->timeattack)
 			&& mapheaderinfo[mapnum]->cup != cup)
 			return false;
@@ -90,6 +90,12 @@ boolean M_CanShowLevelInList(INT16 mapnum, levelsearch_t *levelsearch)
 	// Finally, the most complex check: does the map have lock conditions?
 	if (levelsearch->checklocked)
 	{
+		// Check for visitation
+		if (!(mapheaderinfo[mapnum]->menuflags & LF2_NOVISITNEEDED)
+		&& !(mapheaderinfo[mapnum]->records.mapvisited & MV_VISITED)
+		&& !(cup && cup->cachedlevels[0] == mapnum))
+			return false;
+
 		// Check for completion
 		if ((mapheaderinfo[mapnum]->menuflags & LF2_FINISHNEEDED)
 		&& !(mapheaderinfo[mapnum]->records.mapvisited & MV_BEATEN))
@@ -128,22 +134,9 @@ UINT16 M_CountLevelsToShowInList(levelsearch_t *levelsearch)
 
 	for (i = 0; i < nummapheaders; i++)
 	{
-		if (M_CanShowLevelInList(i, levelsearch))
-		{
-			count++;
-
-			// Tutorial will only show what you've made your way to
-			if (!levelsearch->checklocked)
-				continue;
-			if (!levelsearch->tutorial)
-				continue;
-			if (i >= basenummapheaders)
-				continue;
-			if (mapheaderinfo[i]->records.mapvisited & MV_BEATEN)
-				continue;
-
-			break;
-		}
+		if (!M_CanShowLevelInList(i, levelsearch))
+			continue;
+		count++;
 	}
 
 	return count;
@@ -206,13 +199,6 @@ UINT16 M_GetNextLevelInList(UINT16 mapnum, UINT8 *i, levelsearch_t *levelsearch)
 	}
 	else
 	{
-		// Tutorial will only show what you've made your way to
-		if (levelsearch->checklocked
-		&& levelsearch->tutorial
-		&& mapnum < basenummapheaders
-		&& !(mapheaderinfo[mapnum]->records.mapvisited & MV_BEATEN))
-			return NEXTMAP_INVALID;
-
 		mapnum++;
 		while (!M_CanShowLevelInList(mapnum, levelsearch) && mapnum < nummapheaders)
 			mapnum++;
diff --git a/src/s_sound.c b/src/s_sound.c
index 142eaa4ba..562e05bcc 100644
--- a/src/s_sound.c
+++ b/src/s_sound.c
@@ -1393,11 +1393,13 @@ static boolean S_SoundTestDefLocked(musicdef_t *def)
 
 	mapheader_t *header = mapheaderinfo[def->sequence.map];
 
-	// Is the level tied to SP progression?
-	if ((
-		(header->menuflags & (LF2_FINISHNEEDED|LF2_HIDEINMENU))
-		|| (def->sequence.altref == ALTREF_REQUIRESBEATEN) // Associated music only when completed
-	)
+	// Visitation required?
+	if (!(header->menuflags & LF2_NOVISITNEEDED)
+	&& !(header->records.mapvisited & MV_VISITED))
+		return true;
+
+	// Associated music only when completed
+	if ((def->sequence.altref == ALTREF_REQUIRESBEATEN)
 	&& !(header->records.mapvisited & MV_BEATEN))
 		return true;