diff --git a/programs/zstdcli.c b/programs/zstdcli.c
index 4ea9034a1..9dd6b051a 100644
--- a/programs/zstdcli.c
+++ b/programs/zstdcli.c
@@ -962,7 +962,7 @@ int main(int argCount, const char* argv[])
                 if (!strcmp(argument, "--help")) { usageAdvanced(programName); CLEAN_RETURN(0); }
                 if (!strcmp(argument, "--verbose")) { g_displayLevel++; continue; }
                 if (!strcmp(argument, "--quiet")) { g_displayLevel--; continue; }
-                if (!strcmp(argument, "--stdout")) { forceStdout=1; outFileName=stdoutmark; removeSrcFile=0; continue; }
+                if (!strcmp(argument, "--stdout")) { forceStdout=1; outFileName=stdoutmark; continue; }
                 if (!strcmp(argument, "--ultra")) { ultra=1; continue; }
                 if (!strcmp(argument, "--check")) { FIO_setChecksumFlag(prefs, 2); continue; }
                 if (!strcmp(argument, "--no-check")) { FIO_setChecksumFlag(prefs, 0); continue; }
@@ -1367,14 +1367,6 @@ int main(int argCount, const char* argv[])
 #endif
     }
 
-    /* disable --rm when writing to stdout */
-    if (!strcmp(outFileName, stdoutmark)) {
-        if (removeSrcFile) {
-            DISPLAYLEVEL(2, "warning: source not removed when writing to stdout \n");
-            removeSrcFile = 0;
-        }
-    }
-
     /* Check if benchmark is selected */
     if (operation==zom_bench) {
 #ifndef ZSTD_NOBENCH
diff --git a/tests/playTests.sh b/tests/playTests.sh
index bf5fba89b..dc7794654 100755
--- a/tests/playTests.sh
+++ b/tests/playTests.sh
@@ -234,12 +234,23 @@ unset ZSTD_CLEVEL
 println "test : compress to stdout"
 zstd tmp -c > tmpCompressed
 zstd tmp --stdout > tmpCompressed       # long command format
-println "test : compress to named file"
+
+println "test : compress to named file (-o)"
 rm -f tmpCompressed
 zstd tmp -o tmpCompressed
 test -f tmpCompressed   # file must be created
+
 println "test : force write, correct order"
 zstd tmp -fo tmpCompressed
+
+println "test : -c + -o : last one wins"
+rm -f tmpOut
+zstd tmp -c > tmpCompressed -o tmpOut
+test -f tmpOut   # file must be created
+rm -f tmpCompressed
+zstd tmp -o tmpOut -c > tmpCompressed
+test -f tmpCompressed   # file must be created
+
 println "test : forgotten argument"
 cp tmp tmp2
 zstd tmp2 -fo && die "-o must be followed by filename "
@@ -394,6 +405,8 @@ println "test: --rm is disabled when output is stdout"
 test -f tmp
 zstd --rm tmp -c > $INTOVOID
 test -f tmp # tmp shall still be there
+zstd --rm tmp --stdout > $INTOVOID
+test -f tmp # tmp shall still be there
 zstd -f --rm tmp -c > $INTOVOID
 test -f tmp # tmp shall still be there
 zstd -f tmp -c > $INTOVOID --rm
@@ -411,7 +424,22 @@ zstd -f tmp tmp2 -o tmp3.zst --rm # just warns, no prompt
 test -f tmp
 test -f tmp2
 zstd -q tmp tmp2 -o tmp3.zst --rm && die "should refuse to concatenate"
-
+println "test: --rm is active with -o when single input"
+rm -f tmp2.zst
+zstd --rm tmp2 -o tmp2.zst
+test -f tmp2.zst
+test ! -f tmp2
+println "test: -c followed by -o => -o wins, so --rm remains active" # (#3719)
+rm tmp2.zst
+cp tmp tmp2
+zstd --rm tmp2 -c > $INTOVOID -o tmp2.zst
+test ! -f tmp2
+println "test: -o followed by -c => -c wins, so --rm is disabled" # (#3719)
+rm tmp3.zst
+cp tmp tmp2
+zstd -v --rm tmp2 -o tmp2.zst -c > tmp3.zst
+test -f tmp2
+test -f tmp3.zst
 println "test : should quietly not remove non-regular file"
 println hello > tmp
 zstd tmp -f -o "$DEVDEVICE" 2>tmplog > "$INTOVOID"