diff --git a/spec/20-http_request_header_format.md b/spec/20-http_request_header_format.md
index 64e5f21..a0d6866 100644
--- a/spec/20-http_request_header_format.md
+++ b/spec/20-http_request_header_format.md
@@ -185,7 +185,7 @@ There are two additional options that vendors MAY follow:
 The second least significant bit of the trace-flags field denotes the `random-trace-id` flag.
 
 When starting or restarting a trace (that is, when the participant generates a new `trace-id`), the following rules apply:
-* If that flag is set, at least the right-most 7 bytes of the `trace-id` MUST be random (or pseudo-random).
+* If that flag is set, at least the right-most 7 bytes of the `trace-id` MUST be selected randomly (or pseudo-randomly) with uniform distribution over the interval [0..2^56-1].
 * If the flag is not set, the `trace-id` MAY still be randomly (or pseudo-randomly) generated.
 * When unset, the `trace-id` MAY be generated in any way that satisfies the requirements of the [trace ID format](#trace-id).
 * When at least the right-most 7 bytes of the `trace-id` are randomly (or pseudo-randomly) generated, the `random-trace-id` flag SHOULD be set to `1`.
diff --git a/spec/60-trace-id-format.md b/spec/60-trace-id-format.md
index 4c73363..79ea58a 100644
--- a/spec/60-trace-id-format.md
+++ b/spec/60-trace-id-format.md
@@ -23,7 +23,8 @@ also allows tracing vendors to base sampling decisions on `trace-id` field value
 and avoid propagating an additional sampling context.
 
 If the `random-trace-id` flag is set, at least the right-most 7 bytes of the
-`trace-id` MUST be randomly (or pseudo-randomly) generated.
+`trace-id` MUST be selected randomly (or pseudo-randomly) with uniform distribution
+over the interval [0..2^56-1].
 
 As shown in the next section, if part of the `trace-id` is nonrandom,
 it is important for the random part of the `trace-id` to be as far right in the