diff --git a/NEWS b/NEWS
index 91083160c..c2efd9976 100644
--- a/NEWS
+++ b/NEWS
@@ -13,6 +13,9 @@ Any uppercase BUG_* names are modernish shell bug IDs.
 - Fixed a crash that could occur when a KEYBD trap was set and a multi-line
   command substitution was input in an interactive shell.
 
+- The shell linter's warnings for obsolete arithmetic operators in [[ ... ]]
+  and unnecessary variable expansion in ((...)) have been improved.
+
 2021-11-24:
 
 - The --posix mode was amended to stop the '.' command (but not 'source') from
diff --git a/src/cmd/ksh93/data/lexstates.c b/src/cmd/ksh93/data/lexstates.c
index 2465e268a..19a8dd7c4 100644
--- a/src/cmd/ksh93/data/lexstates.c
+++ b/src/cmd/ksh93/data/lexstates.c
@@ -430,13 +430,13 @@ const char e_lexsyntax2[]	= "syntax error: `%s' %s";
 const char e_lexsyntax3[]	= "syntax error at line %d: duplicate label %s";
 const char e_lexsyntax4[]	= "syntax error at line %d: invalid reference list";
 const char e_lexsyntax5[]	= "syntax error at line %d: `<<%s' here-document not contained within command substitution";
-const char e_lexwarnvar[]	= "line %d: variable expansion makes arithmetic evaluation less efficient";
+const char e_lexwarnvar[]	= "line %d: in '((%s))', using '$' is slower and can introduce rounding errors";
 const char e_lexlabignore[]	= "line %d: label %s ignored";
 const char e_lexlabunknown[]	= "line %d: %s unknown label";
 const char e_lexobsolete1[]	= "line %d: `...` obsolete, use $(...)";
 const char e_lexobsolete2[]	= "line %d: -a obsolete, use -e";
 const char e_lexobsolete3[]	= "line %d: '=' obsolete, use '=='";
-const char e_lexobsolete4[]	= "line %d: %s within [[ ... ]] obsolete, use ((...))";
+const char e_lexobsolete4[]	= "line %d: [[ ... %s ... ]] obsolete, use ((... %s ...))";
 const char e_lexobsolete5[]	= "line %d: set %s obsolete";
 const char e_lexobsolete6[]	= "line %d: `{' instead of `in' is obsolete";
 const char e_lexusebrace[]	= "line %d: use braces to avoid ambiguities with $id[...]";
diff --git a/src/cmd/ksh93/sh/lex.c b/src/cmd/ksh93/sh/lex.c
index 073162bc2..b77577b87 100644
--- a/src/cmd/ksh93/sh/lex.c
+++ b/src/cmd/ksh93/sh/lex.c
@@ -1389,7 +1389,32 @@ breakloop:
 			if(lp->lex.testop2)
 			{
 				if(lp->lexd.warn && (c&TEST_ARITH))
-					errormsg(SH_DICT,ERROR_warn(0),e_lexobsolete4,shp->inlineno,state);
+				{
+					char *alt;
+					switch(c)
+					{
+					    case TEST_EQ:
+						alt = "==";  /* '-eq' --> '==' */
+						break;
+					    case TEST_NE:
+						alt = "!=";  /* '-ne' --> '!=' */
+						break;
+					    case TEST_LT:
+						alt = "<";   /* '-lt' --> '<' */
+						break;
+					    case TEST_GT:
+						alt = ">";   /* '-gt' --> '>' */
+						break;
+					    case TEST_LE:
+						alt = "<=";  /* '-le' --> '<=' */
+						break;
+					    case TEST_GE:
+						alt = ">=";  /* '-ge' --> '>=' */
+						break;
+					}
+					errormsg(SH_DICT, ERROR_warn(0), e_lexobsolete4,
+							shp->inlineno, state, alt);
+				}
 				if(c&TEST_STRCMP)
 					lp->lex.incase = 1;
 				else if(c==TEST_REP)
diff --git a/src/cmd/ksh93/sh/parse.c b/src/cmd/ksh93/sh/parse.c
index 0f7373184..bf4ba8edf 100644
--- a/src/cmd/ksh93/sh/parse.c
+++ b/src/cmd/ksh93/sh/parse.c
@@ -303,7 +303,7 @@ static Shnode_t *getanode(Lex_t *lp, struct argnod *ap)
 	else
 	{
 		if(sh_isoption(SH_NOEXEC) && (ap->argflag&ARG_MAC) && paramsub(ap->argval))
-			errormsg(SH_DICT,ERROR_warn(0),e_lexwarnvar,lp->sh->inlineno);
+			errormsg(SH_DICT,ERROR_warn(0),e_lexwarnvar,lp->sh->inlineno,ap->argval);
 		t->ar.arcomp = 0;
 	}
 	return(t);