diff --git a/docs/liquidity.md b/docs/liquidity.md
index db273055..5427fe97 100644
--- a/docs/liquidity.md
+++ b/docs/liquidity.md
@@ -175,11 +175,11 @@ As in Michelson, there are different types of integers:
     a `tz` suffix (`1.00tz`, etc.) or as a string with type coercion
     (`("1.00" : tez)`).
 
-Timestamps are written in ISO 8601 format or integer seconds since epoch, the
-following are equivalent:
+Timestamps are written in ISO 8601 format, like in Michelson:
 * `("2015-12-01T10:01:00+01:00" : timestamp)`
-* `("1448960460" : timestamp)`
-* `(1448960460 : timestamp)`
+
+Keys and signatures constants are the same as the ones in Michelson:
+* `("tz1hxLtJnSYCVabeGio3M87Yp8ChLF9LFmCM" : key)`
 
 There are also three types of collections: lists, sets and
 maps. Constants collections can be created directly:
diff --git a/tools/liquidity/liquidCheck.ml b/tools/liquidity/liquidCheck.ml
index fc9a0f2f..d3cb47e5 100644
--- a/tools/liquidity/liquidCheck.ml
+++ b/tools/liquidity/liquidCheck.ml
@@ -1371,16 +1371,11 @@ let check_const_type ~to_tez loc ty cst =
     | Ttez, CString s -> CTez (to_tez s)
 
     | Tkey, CKey s
-      | Tkey, CString s -> CKey s
-
-    | Ttimestamp, CInt { integer = s }
-    | Ttimestamp, CNat { integer = s } -> CTimestamp s
+    | Tkey, CString s -> CKey s
 
     | Ttimestamp, CString s
     | Ttimestamp, CTimestamp s ->
       begin (* approximation of correct tezos timestamp *)
-        try Scanf.sscanf s "%_d%!" ()
-        with _ ->
         try Scanf.sscanf s "%_d-%_d-%_dT%_d:%_d:%_dZ%!" ()
         with _ ->
         try Scanf.sscanf s "%_d-%_d-%_d %_d:%_d:%_dZ%!" ()
diff --git a/tools/liquidity/with-tezos/liquidToTezos.ml b/tools/liquidity/with-tezos/liquidToTezos.ml
index 4c5bf18f..a66c2988 100644
--- a/tools/liquidity/with-tezos/liquidToTezos.ml
+++ b/tools/liquidity/with-tezos/liquidToTezos.ml
@@ -62,6 +62,9 @@ let rec convert_const expr =
    | CSignature _|CLeft _|CRight _)
             *)
   | CTimestamp s -> Script_repr.String (0, s)
+  | CKey s -> Script_repr.String (0, s)
+  | CSignature s -> Script_repr.String (0, s)
+
   | _ ->
     LiquidLoc.raise_error "to-tezos: unimplemented const:\n%s%!"
       (LiquidPrinter.Michelson.string_of_const expr)