diff --git a/docs/WHATSNEW b/docs/WHATSNEW
index 6c4b1de9..723ff55b 100644
--- a/docs/WHATSNEW
+++ b/docs/WHATSNEW
@@ -1,5 +1,10 @@
 CHANGES TO REMIND
 
+- CHANGE: The "-tn" option sets all REM statement deltas to ++n rather than
+  adding n to any existing REM statement's delta.  Additionally, the
+  corresponding system variable $DeltaOffset has been renamed to
+  $DeltaOverride.
+
 * VERSION 4.2 Patch 5 - 2023-04-11
 
 - MINOR IMPROVEMENT: remind: If someone uses OMIT yyyy-mm-dd UNTIL yyyy-mm-dd
diff --git a/man/remind.1.in b/man/remind.1.in
index 41dc7214..13344271 100644
--- a/man/remind.1.in
+++ b/man/remind.1.in
@@ -222,8 +222,8 @@ regardless of the \fIdelta\fR supplied for each reminder.
 .TP
 .B \-t\fR\fIn\fR
 If you supply a number \fIn\fR after the \fB\-t\fR option, then
-\fBRemind\fR pretends that \fIn\fR has been \fIadded\fR to each REM statement's
-existing delta and triggers reminders accordingly.
+\fBRemind\fR pretends that echo \fBREM\fR command has a delta
+of \+\+\fIn\fR, regardles of any existing delta.
 .TP
 .B \-tz\fR
 If you supply the letter \fBz\fR after the \fB\-t\fR option, then
diff --git a/src/dorem.c b/src/dorem.c
index 6f39c51f..c99a0fee 100644
--- a/src/dorem.c
+++ b/src/dorem.c
@@ -1200,19 +1200,28 @@ int ShouldTriggerReminder(Trigger *t, TimeTrig *tim, int dse, int *err)
     /* If "infinite delta" option is chosen, always trigger future reminders */
     if (InfiniteDelta || NextMode) return 1;
 
-    /* If there's a "warn" function, it overrides any deltas */
+    /* If there's a "warn" function, it overrides any deltas except
+     * DeltaOverride*/
     if (t->warn[0] != 0) {
-	if (DeltaOffset > 0) {
-	    if (dse <= DSEToday + DeltaOffset) {
+	if (DeltaOverride > 0) {
+	    if (dse <= DSEToday + DeltaOverride) {
 		return 1;
 	    }
 	}
 	return ShouldTriggerBasedOnWarn(t, dse, err);
     }
 
+    /* Zero delta */
+    if (DeltaOverride < 0) {
+        return dse == DSEToday;
+    }
+
     /* Move back by delta days, if any */
-    if (t->delta != NO_DELTA && DeltaOffset >= 0) {
-	if (t->delta < 0)
+    if (DeltaOverride) {
+        /* A positive DeltaOverride takes precedence over everything */
+        dse = dse - DeltaOverride;
+    } else if (t->delta != NO_DELTA) {
+        if (t->delta < 0)
 	    dse = dse + t->delta;
 	else {
 	    int iter = 0;
@@ -1236,11 +1245,8 @@ int ShouldTriggerReminder(Trigger *t, TimeTrig *tim, int dse, int *err)
 	}
     }
 
-    if (DeltaOffset < 0) {
-        return dse == DSEToday;
-    }
     /* Should we trigger the reminder? */
-    return (dse <= DSEToday + DeltaOffset);
+    return (dse <= DSEToday);
 }
 
 /***************************************************************/
diff --git a/src/globals.h b/src/globals.h
index b914c6e9..19d9bcb3 100644
--- a/src/globals.h
+++ b/src/globals.h
@@ -70,7 +70,7 @@ EXTERN  INIT(	int 	Hush, 0);
 EXTERN  INIT(	int 	NextMode, 0);
 EXTERN  INIT(	int 	InfiniteDelta, 0);
 EXTERN  INIT(   int     DefaultTDelta, 0);
-EXTERN  INIT(   int     DeltaOffset, 0);
+EXTERN  INIT(   int     DeltaOverride, 0);
 EXTERN  INIT(   int     RunDisabled, 0);
 EXTERN  INIT(   int     IgnoreOnce, 0);
 EXTERN  INIT(   int     SortByTime, 0);
diff --git a/src/init.c b/src/init.c
index a3e4ccfd..2bbb2b45 100644
--- a/src/init.c
+++ b/src/init.c
@@ -342,12 +342,12 @@ void InitRemind(int argc, char const *argv[])
 		    InfiniteDelta = 1;
 		} else {
                     if (*arg == 'z') {
-                        DeltaOffset = -1;
+                        DeltaOverride = -1;
                         arg++;
                     } else {
-                        PARSENUM(DeltaOffset, arg);
-                        if (DeltaOffset < 0) {
-                            DeltaOffset = 0;
+                        PARSENUM(DeltaOverride, arg);
+                        if (DeltaOverride < 0) {
+                            DeltaOverride = 0;
                         }
                     }
 		}
diff --git a/src/var.c b/src/var.c
index 46514af7..eb48ee6b 100644
--- a/src/var.c
+++ b/src/var.c
@@ -792,7 +792,7 @@ static SysVar SysVarArr[] = {
     {"DefaultColor",   1,  SPECIAL_TYPE, default_color_func,   0,      0 },
     {"DefaultPrio",    1,  INT_TYPE,     &DefaultPrio,         0,      9999 },
     {"DefaultTDelta",  1,  INT_TYPE,     &DefaultTDelta,       0,      1440 },
-    {"DeltaOffset",    0,  INT_TYPE,     &DeltaOffset,         0,      0 },
+    {"DeltaOverride",  0,  INT_TYPE,     &DeltaOverride,         0,      0 },
     {"DontFork",       0,  INT_TYPE,     &DontFork,            0,      0 },
     {"DontQueue",      0,  INT_TYPE,     &DontQueue,           0,      0 },
     {"DontTrigAts",    0,  INT_TYPE,     &DontIssueAts,        0,      0 },
diff --git a/tests/test-rem b/tests/test-rem
index 5740d2e6..9916b5b0 100644
--- a/tests/test-rem
+++ b/tests/test-rem
@@ -408,6 +408,14 @@ TZ=Europe/Berlin ../src/remind -dxe ../tests/tz.rem >> ../tests/test.out 2>&1
 # Test that banner is printed on every iteration
 echo "MSG Should be three banners." | ../src/remind - 2022-10-20 '*3' >> ../tests/test.out 2>&1
 
+# Test the -tn option
+echo "REM May 23 +10 MSG Orange %b" | ../src/remind - 2023-05-21 >> ../tests/test.out 2>&1
+echo "REM May 23 +10 MSG Quux %b" | ../src/remind -t1 - 2023-05-21 >> ../tests/test.out 2>&1
+echo "REM May 23 +10 MSG Cabbage %b" | ../src/remind -t2 - 2023-05-21 >> ../tests/test.out 2>&1
+echo "REM May 23 MSG Banana %b" | ../src/remind - 2023-05-21 >> ../tests/test.out 2>&1
+echo "REM May 23 MSG Carrot %b" | ../src/remind -t1 - 2023-05-21 >> ../tests/test.out 2>&1
+echo "REM May 23 MSG Apple %b" | ../src/remind -t2 - 2023-05-21 >> ../tests/test.out 2>&1
+
 # Test the -tz option
 echo "REM May 22 +10 MSG Foo %b" | ../src/remind - 2023-05-21 >> ../tests/test.out 2>&1
 echo "REM May 22 +10 MSG Bar %b" | ../src/remind -tz - 2023-05-21 >> ../tests/test.out 2>&1
diff --git a/tests/test.cmp b/tests/test.cmp
index adae26ca..63f43af9 100644
--- a/tests/test.cmp
+++ b/tests/test.cmp
@@ -2756,7 +2756,7 @@ Variable  Value
    $DefaultColor  "-1 -1 -1"
     $DefaultPrio  5000        [0, 9999]
   $DefaultTDelta  0           [0, 1440]
-    $DeltaOffset  0
+  $DeltaOverride  0
        $DontFork  0
       $DontQueue  1
     $DontTrigAts  0
@@ -2883,9 +2883,9 @@ msg [$DefaultTDelta]%
 ../tests/test.rem(484): Trig = Saturday, 16 February, 1991
 $DefaultTDelta => 0
 0
-msg [$DeltaOffset]%
+msg [$DeltaOverride]%
 ../tests/test.rem(485): Trig = Saturday, 16 February, 1991
-$DeltaOffset => 0
+$DeltaOverride => 0
 0
 msg [$DontFork]%
 ../tests/test.rem(486): Trig = Saturday, 16 February, 1991
@@ -10545,6 +10545,21 @@ Should be three banners.
 
 Reminders for Sunday, 21st May, 2023:
 
+Orange in 2 days' time
+
+No reminders.
+Reminders for Sunday, 21st May, 2023:
+
+Cabbage in 2 days' time
+
+No reminders.
+No reminders.
+Reminders for Sunday, 21st May, 2023:
+
+Apple in 2 days' time
+
+Reminders for Sunday, 21st May, 2023:
+
 Foo tomorrow
 
 No reminders.
diff --git a/tests/test.rem b/tests/test.rem
index 833846d6..08265ee5 100644
--- a/tests/test.rem
+++ b/tests/test.rem
@@ -482,7 +482,7 @@ msg [$December]%
 msg [$DefaultColor]%
 msg [$DefaultPrio]%
 msg [$DefaultTDelta]%
-msg [$DeltaOffset]%
+msg [$DeltaOverride]%
 msg [$DontFork]%
 msg [$DontQueue]%
 msg [$DontTrigAts]%